The required in order for Micaela to end up with ,n = 365 , t = 12, P = $360, and A = $670
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A binary relation from A to B is made up of these ordered pairs (a,b),
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), here the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
According to our question-
r=7.5%
Thus, 7.5% would be required in order for Micaela to end up with $670.
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A radio station has a broadcast area in the shape of a circle with equation x^2+y^2=5,625, where the constant represents square miles.
a. Find the intercepts of the graph.
b. State the radius in miles.
c. What is the area of the region in which the broadcast from the station can be picked up?
Show all work please!!
Answer:
a) The intercepts of the graph are (-75, 0), (75, 0), (0, -75) and (0, 75).
b) The radius is 75 miles.
c) The area of the region is 17,671 square miles (to the nearest square mile).
Step-by-step explanation:
Part aThe x-intercepts are the points at which the graph crosses the x-axis, so when y = 0. Therefore, to find the x-intercepts, substitute y = 0 into the given equation.
[tex]\implies x^2+y^2=5625[/tex]
[tex]\implies x^2+(0)^2&=5625[/tex]
[tex]\implies x^2&=5625[/tex]
[tex]\implies x&=\sqrt{5625}[/tex]
[tex]\implies x&=\pm75[/tex]
The y-intercepts are the points at which the graph crosses the y-axis, so when x = 0. Therefore, to find the y-intercepts, substitute x = 0 into the given equation.
[tex]\implies x^2+y^2=5625[/tex]
[tex]\implies (0)^2+y^2&=5625[/tex]
[tex]\implies y^2&=5625[/tex]
[tex]\implies y&=\sqrt{5625}[/tex]
[tex]\implies y&=\pm75[/tex]
Therefore, the intercepts of the graph are:
(-75, 0), (75, 0), (0, -75) and (0, 75)[tex]\hrulefill[/tex]
Part bThe general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h, k) is the center and r is the radius of the circle.
By comparing the given equation with the general equation:
(h, k) = (0, 0)r² = 5625Take the positive square root of r² to find the radius of the circle (since length cannot be negative):
[tex]\implies r=\sqrt{5625}[/tex]
[tex]\implies r=75[/tex]
Therefore, the radius of the circle is 75 miles.
[tex]\hrulefill[/tex]
Part cThe formula for the area of a circle is:
[tex]A=\pi r^2[/tex]
where r is the radius.
To find the area of the region in which the broadcast from the station can be picked up, find the area of the circle with the radius from part b, r = 75:
[tex]\implies A= \pi \cdot 75^2[/tex]
[tex]\implies A=5625 \pi[/tex]
[tex]\implies A=17671.4586...[/tex]
Therefore, the area of the region is 17,671 square miles (to the nearest square mile).
Answer:
(75,0) ; (-75,0) ; (0,75) ; (0,-75)75 miles 17678.51 miles²Step-by-step explanation:
To find:-
The intercepts of the graph .Radius in miles.Area of the region.Answer:-
The given equation of the circle is ,
[tex]:\sf\implies x^2 + y^2 = 5625 \\[/tex]
[tex]\rule{200}2[/tex]
G R A P H : -
[tex]\setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\vector(1,0){6}}\put(0,0){\vector(-1,0){6}}\put(0,0){\vector(0,1){6}}\put(0,0){\vector(0,-1){6}}\put(.2,2.5){$\sf (0,75)$}\put(.2, - 2.7){$\sf (0,-75)$}\put(2.5,0.2){$\sf (75,0)$}\put( - 4.2,.2){$\sf ( - 75,0)$}\put(4,4){$\bigstar \: \: \sf Centre = (0,0) $}\put(4,3){$\bigstar \: \: \sf Radius = 75\ miles $}\put(4,-4){$\boxed{\bf \textcopyright \: \: Tony Stark }$}\end{picture}[/tex]
[tex]\rule{200}2[/tex]
Answer a :-
The intercepts are the points at which the circle cuts the x-axis and y-axis . At x intercept , the value of y coordinate becomes 0 and at y intercept the x coordinate becomes 0 .
So for finding x intercept , plug in y = 0 , in the given equation of circle, as ;
[tex]:\sf\implies x^2 + (0)^2 = 5625 \\[/tex]
[tex]:\sf\implies x^2 = 5625 \\[/tex]
[tex]:\sf\implies x =\sqrt{5625} \\[/tex]
[tex]:\sf\implies x =\pm 75 \\[/tex]
[tex]:\sf\implies \red{ x = +75 , -75} \\[/tex]
Hence the circle cuts the x-axis at (75,0) and (-75,0).
To find out y intercept plug in x = 0 in the given equation of the circle as ,
[tex]:\sf\implies (0)^2 + y^2 = 5625 \\[/tex]
[tex]:\sf\implies y^2 = 5625 \\[/tex]
[tex]:\sf\implies y=\sqrt{5626}\\[/tex]
[tex]:\sf\implies y = \pm 75 \\[/tex]
[tex]:\sf\implies \red{ y = +75,-75} \\[/tex]
Hence the circle cuts the y-axis at (0,75) and (0,-75).
[tex]\rule{200}2[/tex]
Answer b :-
Next we are interested in finding out the radius of the circle, for that we need to compare the given equation of circle to the standard equation of circle .
Standard equation of circle :-
[tex]:\sf\implies \red{ (x-h)^2 + (y-k)^2 = r^2}[/tex]
where ,
(h,k) is the centre of the circle.r is the radius.We can rewrite the given equation of circle as ,
[tex]:\sf\implies (x-0)^2 + (y-0)^2 = 5625 \\[/tex]
[tex]:\sf\implies (x-0)^2+(y-0)^2 = 75^2\\[/tex]
On comparing to the standard form, we have;
[tex]:\sf\implies \red{ radius = 75\ miles } \\[/tex]
Hence the radius of the circle is 75miles .
[tex]\rule{200}2[/tex]
Answer c :-
To find out the area we can use the formula of area of circle , which is ;
[tex]:\sf\implies \red{Area=\pi(radius)^2} \\[/tex]
We already got the radius to be 75 miles in the previous part of the question. Plugging in that value would give us the area , as ;
[tex]:\sf\implies Area =\pi (75\ miles )^2 \\[/tex]
[tex]:\sf\implies Area = \dfrac{22}{7}\times 5625\ miles^2\\[/tex]
[tex]:\sf\implies \red{ Area = 17678.57 \ miles^2 } \\[/tex]
Hence the area of the circle is 17678.57 miles² .
Pancake Paradise makes the best Pineapple Pancakes. Each Pancake has an diameter of 2.5 inches. Each batch contains enough batter to cover an area of 15 inches.
How many whole pancakes does each batch make?
If Pancake Paradise makes the best Pineapple Pancakes. Each batch makes 3 whole pancakes.
How many does each batch makes 3 whole pancakes?To find the number of whole pancakes in each batch, we need to first calculate the area of one pancake.
The diameter of each pancake is 2.5 inches, which means the radius is 1.25 inches (diameter = 2 x radius). The area of each pancake is:
A = πr^2 = π(1.25 in)^2 ≈ 4.91 in^2
Next, we need to determine how many pancakes can be made from a batch of batter that covers an area of 15 inches.
Number of pancakes = Total area / Area of one pancake
Number of pancakes = 15 in^2 / 4.91 in^2 ≈ 3.05
Since we can't make a fraction of a pancake, we need to round down to the nearest whole number. Therefore, each batch makes 3 whole pancakes.
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There are 3 items in an order. They cost $8.95, $11.49, and $12.75. The sales tax for this order is 6.5%.
What is the total cost of the order?
Responses
$33.19
$35.35
$49.79
$54.76
Answer:
$35.35
Step-by-step explanation:
First, let's add all these prices together:
$8.95 + $11.49 + $12.75 = $33.19
Then, let's find how much will the whole price increase with the taxes:
[tex] \frac{33.19 \times 6.5\%}{100\%} = 2.15735[/tex]
And finally, let's add this number and the old price together:
$33.19 + $2.15735 = $35.34735 ≈ $35.35
if a person 12 ft above water is pulling a rope 6 ft per minture how fast is the boat moving when 16 ft from the pier
If person is standing at the end of a pier 12 ft above the water, then the velocity of the boat when it is 16 ft from the pier is 7.5 ft/min.
The distance between the person and the water (y) = 12 ft,
The distance between the boat and the pier is (x) = 16 ft,
So, p = √(12² + 16²) = 20 ft,
From the triangle given below,
⇒ x² + y² = p²,
taking "derivative" with respect to "x",
We get,
⇒ 2x(dx/dt) + 2y(dy/dt) = 2p(dp/dt);
⇒ dy/dt = 0 ..because height is constant,
The water is pulling on a rope at speed of (dp/dt) = 6 ft/min,
⇒ 2x(dx/dt) = 2p(dp/dt),
⇒ 2×16×(dx/dt) = 2×20×6,
⇒ dx/dt = 7.5 ft/min.
Therefore, the velocity of the boat is 7.5ft/min.
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The given question is incomplete, the complete question is
A person is standing at the end of a pier 12 ft above the water and is pulling on a rope attached to a rowboat at the waterline at a rate of 6 ft per minute. What is the velocity of the boat when it is 16 ft from the pier?
43 ÷ 2 – 3.6(14.1 – 8.7)
Answer:
Step-by-step explanation:
the answer willbe 80
A study on students drinking habits wants to determine the true average number of alcoholic drinks all UF "greek" students have in a one week! period. We know from preliminary studies that the standard deviation is around 6.3. How many students should be sampled to be within 0.5 drink! of population mean with 95% probability? 609 *305 304 610
Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.
To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error
Margin of error = Z × (standard deviation / sqrt(sample size))
where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.
We want the margin of error to be no more than 0.5 drinks, so we can set up the equation
0.5 = 1.96 × (6.3 / sqrt(sample size))
Solving for the sample size, we get
sqrt(sample size) = 1.96 × 6.3 / 0.5
sqrt(sample size) = 24.82
sample size = (24.82)^2
sample size = 617
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What is the best move?
Answer:
the best move is king because it did not have a king
Is the point (3, 1) a solution to the inequality y<4x+2?
Answer:
1<4(3)+2
1<12+2
1<14
so therefore we say the answer is 1 is lesser than 14
for what values of a are the following expressions true:|a+5|=a+5
Answer:
|a+5|=a+5
Step-by-step explanation:
if a>-5 or a= -5 |a+5|=a+5
if a< -5 |a+5|= -a-5
Shannon was asked to solve 1536÷6 . She decided to break the number down 1,536 into 3 numbers which can be divided by 6 . She divided each of the numbers by 6 and then added the 3 products together for her final answer. Which 3 numbers did Shannon break down 1,536 into and then add the products to get 256 as her answer?
Shannon broke down 1536 into three numbers: 256, 72, and 56, and then added the products of these three numbers to get her final answer of 256.
what is products and addition ?
The product is the result of multiplying two or more numbers together. For example, the product of 2 and 3 is 6, denoted as 2 x 3 = 6.Addition is another arithmetic operation that involves combining two or more numbers to find a total or a sum.
In the given question,
To solve 1536 ÷ 6, Shannon broke down the number 1536 into three numbers that are divisible by 6.
Let's start by finding the factors of 6: 1, 2, 3, and 6.
We need to find three numbers whose sum is equal to 1536 and each of which is divisible by 6.
We can start with the largest factor of 6, which is 6 itself. We can divide 1536 by 6 to get 256.
Now we need to find two more numbers whose sum is 128 and are also divisible by 6.
One such pair of numbers is 72 and 56.
We can verify that the sum of these three numbers is indeed 1536:
256 + 72 + 56 = 384 + 56 = 440 + 256 = 696 + 840 = 1536.
So, Shannon broke down 1536 into three numbers: 256, 72, and 56, and then added the products of these three numbers to get her final answer of 256.
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Do you see a pattern? If so, how many toothpicks would you need to make 10 squares according to your pattern? Can you represent a pattern with an expression?
Answer:
I can see the pattern. There will be 30 toothpicks to make 10 squares accordingto your pattern. The pattern with an expression is +3.
Step-by-step explanation:
If you list the 4,7,10 and see the pattern between these numbers. You are adding 3 to the 4 to the 7 and 7 to the 10. Then, follow the pattern until you get 10 squares.
HELP ASAP PLEASEEE!!!!
In analyzing hits by certain bombs in a war, an area was partitioned into 583 regions, each with an area of 0.85 km2. A total of 505 bombs hit the combined area of 583 regions. Assume that we want to find the probability that a randomly selected region had exactly four hits. In applying the Poisson probability distribution formula, P(x)=μx•e−μx!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
Identify the values of μ, x, and e.
(Type integers or decimals rounded to five decimal places as needed.)
Applying the Poisson probability distribution formula, the values of μ, x, and e are: μ ≈ 0.866, x = 4, and e ≈ 2.71828
What is the probability?To apply the Poisson distribution formula, we need to identify the values of μ, x, and e:
μ is the mean or average number of hits per region. We can calculate μ as the total number of hits divided by the total number of regions:
μ = total number of hits / total number of regions = 505 / 583
μ ≈ 0.866
x is the number of hits we want to find the probability for, which in this case is 4.
e is the mathematical constant e, which is approximately equal to 2.71828 and is used in the Poisson distribution formula to calculate the probability of x hits.
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12(-72)+41(-3 - 32 what is it
Answer:
-2299
Step-by-step explanation:
12(-72) = -864
(-3 - 32) = -35
41(-35) = -1435
-864 + -1435 = -2299
HELPPP DUE SOON!!!!!!
The numbers in scientific notation 3.26E21 and 5.95E-27 are 3.26E21 = 3.26 * 10^21 and 5.95E-27 = 5.95 * 10^-27
How to write the numbers in scientific notationFrom the question, we have the following parameters that can be used in our computation:
3.26E21 and 5.95E-27
A number represented using aEb can be represented as
aEb = a * 10^b
Using the above as a guide, we have the following:
3.26E21 = 3.26 * 10^21
5.95E-27 = 5.95 * 10^-27
Hence, the numbers in scientific notation are 3.26E21 = 3.26 * 10^21 and 5.95E-27 = 5.95 * 10^-27
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Help me please asappppp
Answer:
To fine mean (average) you add up all the numbers and divide it by the amount of numbers. there are 8 scores
Step-by-step explanation:
55+60+65+70+75+80+85+90
=580
580/8=72.5
the mean is 72.5
If U= {a, b, c, d, e, f, g, h, i}, A = {a, b, d, f), B = {a, c, e, f} andC = {d, f, g, h} then (a) Show the relation of U, A, B and C in a Venn-diagram. (b) Find A - (AnBnC)
[Ans: (a, b, d}]
The venn diagram is given below and A - (AnBnC) is {a, b, d}.
What is venn diagram?
A Venn diagram consists of one or more circles, each representing a set. The items that belong to each set are placed inside the appropriate circle, and the overlapping areas between the circles represent items that belong to both sets.
(a) Here's a Venn diagram that shows the relation of U, A, B, and C:
The circle labeled "A" represents the set A, the circle labeled "B" represents the set B, and the circle labeled "C" represents the set C. The regions where the circles overlap represent the elements that are in more than one set.
(b) A - (AnBnC) means the elements that are in set A but not in the intersection of sets A, B, and C. To find these elements, we first need to find the intersection of sets A, B, and C:
AnBnC = {f}
Then, we can subtract that set from set A:
A - (AnBnC) = {a, b, d}
Therefore, A - (AnBnC) is {a, b, d}.
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First, rewrite 19/21 and 8/9 so that they have a common denominator.
we can simply do that by multiplying each by the other's denominator.
[tex]\cfrac{19}{21}\hspace{9em}\cfrac{8}{9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{19}{21}\cdot \cfrac{9}{9}\implies \boxed{\cfrac{171}{189}}\hspace{9em}\cfrac{8}{9}\cdot \cfrac{21}{21}\implies \boxed{\cfrac{168}{189}}[/tex]
Find the thirty-fourth term of the sequence defined by a = 146, a₁ = an-1+ 36.
The thirty-fourth term of the sequence is 1282.
How to find the nth term of any sequence?First, we can find the second term of the ap series as follows:
a₂ = a₁ + 36 = a₄₃ + 36
Similarly, we can find the third term of the sequence as:
a₃ = a₂ + 36 = a₄₄ + 36
Continuing this pattern, we can find the thirty-fourth term of the sequence as:
a₃₄ = a₃₃ + 36 = (a₃₂ + 36) + 36 = ((a₃₁ + 36) + 36) + 36 = so on = a + 33(36)
Substituting the given value of a = 146, we get:
a₃₄ = 146 + 33(36) = 1282
a₃₄ = 1282
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Ian scores 44 out of 60 marks in a Maths test
What is his score as a percentage to 1 decimal place?
Ian's score as a percentage is 73.3%, rounded to one decimal place. This means that he obtained 73.3% of the total marks possible in the test.
The percentages are a useful way to express scores or quantities relative to the whole. In this case, Ian's percentage score indicates how well he performed on the test compared to the maximum score possible.
To calculate Ian's score as a percentage, we can use the formula:
percentage score = (marks obtained / total marks) x 100
In this case, Ian scored 44 out of a total of 60 marks. Plugging these values into the formula, we get:
percentage score = (44 / 60) x 100 = 73.3%
Therefore, Ian's score as a percentage is 73.3%, rounded to one decimal place. This means that he obtained 73.3% of the total marks possible in the test.
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Which function is continuous at x = 18?
x = 18 is given by:
f(x) = (x - 18)²
-------------
x
Or, if you have choices it is CHOICE A :) :P
A city has a population of 28000 people. Suppose that each year the population grows by 4.5%. What will the population be after 13 years?
A city has a population of 28,000 people. Suppose that each year the population grows by 4.5%. What will the population be in 13 years?
Answer: Approximately 496,21 people
This is an exponential growth question, specifically population growth. We will use the following equation to help us solve this situation:
[tex]P(t) = a(1+r)^t[/tex]
[tex]P(t) = \text{total population} \ (??)[/tex]
[tex]\text{a = initial population = 28,000}[/tex]
[tex]\text{r = growth factor (the percent as a decimal) = 0.045}[/tex]
[tex]1 + r = 1 + 0.045 = 1.045[/tex]
[tex]\text{t = time in years = 13}[/tex]
So, we can substitute all our information and solve:
[tex]P(13) = 28,000(1.045)^{13} = 496,21.49[/tex]
Rounding to the nearest whole person, 496,21 people in 13 years.
A water tank is leaking. The amount of water in the tank was measured three times after it started to
leak. The table shows the measurements. (20 points)
Time (t, in minutes) 2 4 9 10 15 20
Amount of water 1900 1800 1500 1430 1045 588
A. Graph the information given in the table. Be sure to label your axes.
B. Based on the graph, what model would you choose to fit this data? Explain.
C. Using your graph, estimate the amount of water left in the tank after 3 minutes.
D. If this pattern were to continue, estimate when the tank will be empty.
The model that fits the data is a linear model and the equation is y = -72.5x + 2102.6
The graph of the informationSee attachment
The model that fits the dataBased on the graph, the model would you choose to fit this data is a linear regression, and the equation is
y = -72.5x + 2102.6
This is because the points appears to be linear
Estimating the amount after three minutesWe have
x = 3
So, we have
y = -72.5 * 3 + 2102.6
y = 1885.1
So, the amount is 1885.1
When it will be emptyHere, we have
y = 0
So, we have
-72.5x + 2102.6 = 0
This gives
x = 29
Hence, the time is 29 minutes
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The sum of the height and radius of a right circular cylinder is 9cm. if the total surface area is 81πcm square , then what is the radius of the cylinder?
The radius of the cylinder is 4.5 cm.
What is a cylinder?
A cylinder is a three-dimensional solid in mathematics that maintains two parallel bases that are separated at a fixed distance by a curving surface. An axis joins the centres of each base, and the bases are often circular in shape.
We are given that the sum of the height and radius of a right circular cylinder is 9 cm.
This means that r + h = 9
We are also given that the total surface area is 81π cm square.
So,
⇒ 81π = 2πr (r + h)
⇒ 81 = 2 * r * 9
⇒ 81 = 18r
⇒ r = 4.5 cm
Hence, the radius of the cylinder is 4.5 cm.
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if the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score e(x y)? (enter your answer to one decimal place.)
The expected recorded score of the given data of short quiz is,
Expected recorded score is 8.5.
And maximum of the two expected recorded score is 12.45.
Expected recorded score e(x + y),
e(x + y) = ΣΣ (x + y) p(x, y)
Simplify this expression by rearranging the sum,
e(x + y) = ΣΣ x p(x, y) + ΣΣ y p(x, y)
Using the table given,
ΣΣ x p(x, y)
= (0×0.02) + (5×0.04) + (10×0.01) + (0×0.06) + (5×0.13) + (15×0.15) + (0×0.02) + (5×0.20) + (10×0.16)
= 4.6
ΣΣ y p(x, y)
= (0×0.02) + (0×0.06) + (0×0.02) + (5×0.10) + (5×0.13) + (5×0.01) + (10×0.20) + (10×0.15) + (10×0.16)
= 3.9
Expected recorded score is,
e(x + y)
= 4.6 + 3.9
= 8.5
The maximum of the two scores is recorded,
Then the recorded score will be either x or y, whichever is larger.
Probability distribution of the maximum score,
P(max(x, y) = 0)
= P(x=0, y=0)
= 0.02
P(max(x, y) = 5)
= P(x=5, y=0) + P(x=0, y=5) + P(x=5, y=5)
= 0.06 + 0.04 + 0.13
= 0.23
P(max(x ,y) = 10)
= P(x=10, y=0) + P(x=0, y=10) + P(x=10, y=5) + P(x=5, y=10) + P(x=10, y=10)
= 0.01 + 0.15 + 0.20 + 0.10 + 0.16
= 0.62
P(max(x, y) = 15)
= P(x=15, y=0) + P(x=0, y=15) + P(x=15, y=5) + P(x=5, y=15) + P(x=15, y=10) + P(x=10, y=15) + P(x=15, y=15)
= 0.01 + 0.10 + 0.10 + 0.10 + 0.01 + 0.01 + 0.01
= 0.34
Expected recorded score can be calculated as the weighted sum of the possible maximum scores,
E(max(x, y)) = Σ max(x, y) × P(max(x, y))
Substituting the probabilities, we get,
E(max(x ,y))
= 0×0.02 + 5×0.23 + 10×0.62 + 15×0.34
= 0+ 1.15 + 6.2 + 5.1
= 12.45
Expected recorded score is 12.45 (upto two decimal places).
Therefore, expected recorded score is 8.5 and maximum of the expected recorded score is 12.45.
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The above question is incomplete, the complete question is:
An instructor has given a short quiz consisting of two parts. for a randomly selected student, let x = the number of points earned on the first part and y = the number of points earned on the second part. suppose that the joint pmf of x and y is given in the accompanying table.
y
p(x, y) 0 5 10 15
0 0.02 0.06 0.02 0.10
x 5 0.04 0.13 0.20 0.10
10 0.01 0.15 0.16 0.01
(a) if the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score e(x + y)? (enter your answer to one decimal place.)
(b) if the maximum of the two scores is recorded, what is the expected recorded score? (enter your answer to two decimal places.)
each year, francesca earns a salary that is 2 % 2%2, percent higher than her previous year's salary. in her first 5 55 years at this job, she earned a total of $ 187 , 345 $187,345dollar sign, 187, comma, 345. what was francesca's salary in her 1 st 1 st 1, start superscript, start text, s, t, end text, end superscript year at this job? round your final answer to the nearest thousand.
Francesca salary in the first year is $169684.14
Let us assume that P be the first salary of Francesca.
The salary increases by 2% every year.
Let A be the amount she earns after n years at a rate of r.
Using the formula for the compound interest is:
A = P (1 + r)ⁿ
Here, A = $187345
n = 5 years
R = 2%
So, r = 0.02
We need to find the value of P
substituting these values in above equation we get,
187345 = P (1.02)⁵
187345 = 1.10408 × P
P = $169684.14
Therefore,her salary in the first year is $169684.14
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The complete question is:
Each year, Francesca earns a salary that is 2 percent higher than her previous year's salary. In her first 5 years at this job, she earned a total of $187,345. What was Francesca's salary in her 1st year at this job?
Identify the equation for a circle with its center at (-10, 4) and a radius length of 2.
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-10}{h}~~,~~\underset{4}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-10) ~~ )^2 ~~ + ~~ ( ~~ y-4 ~~ )^2~~ = ~~2^2\implies (x+10)^2+(y-4)^2=4[/tex]
given 20% chance that any given person walks in the door is wearing N95 mask what is the probability that the first person walk in wearing N95 is the third person
The probability that the first person who walks in wearing an N95 mask is the third person is 0.128 or 12.8%. The probability that the first person who walks in wearing an N95 mask is the third person can be found using the geometric probability distribution formula.
The formula for the probability of the first success occurring on the kth trial is:
P(k) = (1 - p)^(k-1) * p
Where p is the probability of success (in this case, 20% or 0.2), and k is the number of trials.
In this case, we want to find the probability that the third person who walks in is wearing an N95 mask, so k = 3.
Substituting the values, we get:
P(3) = (1 - 0.2)^(3-1) * 0.2
P(3) = 0.64 * 0.2
P(3) = 0.128
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. a baseball diamond is a square with side 90 ft. a batter hits the ball and runs toward first base with a speed of 24 ftys. (a) at what rate is his distance from second base decreasing when he is halfway to first base? (b) at what rate is his distance from third base increasing at the same moment
a. At the moment when the batter is halfway to first base, his distance from second base is not changing.
b. His distance from third base increasing at the same moment at rate 6√2 ft/s.
Let A be the starting point of the batter, B be second base and C be third base, and $P$ be the position of the batter when he is halfway to first base.
Note that AP = AB/2 = 45 ft, B = AB - AP = 45 ft, and PC = AC - AP = 45√2 ft.
(a) We want to find [tex]$\frac{d}{dt} PB$[/tex] when AP = 45 ft and [tex]$\frac{dAP}{dt} = 24$[/tex] ft/s.
By the Pythagorean theorem, we have
PB² = AB² - AP² = 90² - 45² = 4050, so PB = √4050 ft.
To find [tex]$\frac{dPB}{dt}$[/tex] , we take the derivative of both sides of the equation PB² = 4050 with respect to time t:
[tex]2PB\frac{dPB}{dt} &= 0 \\\\\\\frac{dPB}{dt} &= 0[/tex]
Therefore, at the moment when the batter is halfway to first base, his distance from second base is not changing.
(b) We want to find [tex]$\frac{d}{dt} PC$[/tex] when AP = 45 ft and [tex]$\frac{dAP}{dt}[/tex] = 24 ft/s.
By the Pythagorean theorem, we have
PC² = AC² - AP² = (90\√2})² - 45² = 5850,
so PC = √5850 ft.
To find [tex]$\frac{dPC}{dt}$[/tex] we take the derivative of both sides of the equation PC² = 5850 with respect to time t:
[tex]2PC\frac{dPC}{dt} &= 2\frac{dAP}{dt}(AC - AP) \\\\\frac{dPC}{dt} &= \frac{dAP}{dt} \frac{AC - AP}{PC} \&= \frac{24(90\sqrt{2} - 45)}{\sqrt{5850}} \&= 16\sqrt{2} \approx 22.63 \text{ ft/s}.\end{align*}[/tex]
Therefore, at the moment when the batter is halfway to first base, his distance from third base is increasing at a rate of 16√2 ft/s.
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consider the events , , . if a player rolls this weighted die and wins $1 if the outcome is in event , wins $ 2 if the outcome is in event , and loses $3 if the outcome is in event . what is the expected value of this game (how much should a player expect to win or lose)?
Consider the events , , . if a player rolls this weighted die and wins $1 if the outcome is in event , wins $ 2 if the outcome is in event , and loses $3 if the outcome is in event .
The expected value of this game is 0.70. The player should expect to win 0.70.
To find out the expected value of this game, we will use the formula
E(X)= ∑(xP(x))
where X represents the possible outcomes and P(x) represents the probabilities of those outcomes.
Let's determine the probabilities of each event:
Event 1: P(1) = 0.3
Event 2: P(2) = 0.5
Event 3: P(3) = 0.2
Using the information given in the question, we know that a player wins 1 if the outcome is in event 1, wins 2 if the outcome is in event 2, and loses $3 if the outcome is in event 3.
Therefore, the values of each event are:
Event 1: 1
Event 2: 2
Event 3: -3
Now, we can use the formula to calculate the expected value:
E(X)= ∑(xP(x))E(X)
= (1 x 0.3) + (2 x 0.5) + (-3 x 0.2)
E(X) = 0.3 + 1 - 0.6E(X)
= 0.7
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EXPONENTS AND SCIENTIFIC NOTATION Name:
Date:
Pd:
MAZE #1 Instructions: Simplify each expression using properties of exponents to make it correctly through
the maze. Shade or color your path as you go 8th grade math
Each of the expressions has been simplified by using properties of exponents as shown below.
What is an exponent?In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:
(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷
12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴
5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵
6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶
9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸
1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶
(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴
3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷
9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵
3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶
1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.
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