Answer:h<13
Because h has to be less than 13, so h<13 is the correct answer
Step-by-step explanation:
Answer:
it could either be h<13 or 13-h depending on what you're studying
solve the system of inequalities for y+3x<5 and 1>2x-y ?
The shaded region is below both lines, and the boundary line y = 2x - 1 is dashed because the inequality is strict. The solution can be described as: y < 5 - 3x and y < 2x - 1.
What is inequality?Inequality is a mathematical statement that compares two values or expressions. It uses symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to indicate the relationship between the two expressions. Inequalities are used to represent a range of possible values, rather than just a single value as in an equation.
Here,
We have the system of inequalities:
y + 3x < 5
2x - y > 1
To solve this system, we can start by isolating y in each inequality:
y < 5 - 3x
y < 2x - 1
Now we can graph each inequality on the coordinate plane and shade the region that satisfies both inequalities.
For the first inequality y < 5 - 3x, we can start by graphing the line y = 5 - 3x. This line has a y-intercept of 5 and a slope of -3. Since the inequality is y < 5 - 3x, we need to shade the region below the line.
For the second inequality y < 2x - 1, we can start by graphing the line y = 2x - 1. This line has a y-intercept of -1 and a slope of 2. Since the inequality is 2x - y > 1, we need to shade the region below the line.
The solution to the system is the region that is shaded by both inequalities. Here is a graph of the solution:
| /
5 |- - - -/---- - - - - - - -
| / | /
| / | /
2 |- - - - -/------- - - - -
| / | /
|/ | /
-1 | - - - - - - - - - - - - -
0 1 2 3
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Alex wants to fence in an area for a dog park. He has plotted three sides of the fenced area at the points E (1, 5), F (3, 5), and G (6, 1). He has 16 units of fencing. Where could Alex place point H so that he does not have to buy more fencing?
A. (0, 1)
B. (0, −2)
C. (1, 1)
D. (1, −2)
Answer:
C. (1, 1)
Step-by-step explanation:
first lets find how much fencing he has used between the three sides they gave us.
between E and F, there is 2 units.
between F and G, there is sqrt(3^2 + 4^2) = 5 units.
so, lets try option C.
between E and C, there is 4 units.
between C and C and G, there is 5 units.
2 + 5 + 4 + 5 = 16, which is how much fencing he has.
yes, it is C. (1, 1)
Garnet has a container with cups of flour in it. She can make one dozen muffins with cups of flour. How many dozens of muffins can Garnet make with the flour she has?
Answer:
B is correct
Step-by-step explanation:
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 16 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the nearest tenth of a cubic foot?
an elastic belt is placed around therein of a pulley of radius 5 cm one point of the belt is pulled directly away from the centre o of the pulley until its at p , 10 cm from o find the length of the best that is with the contact of rim of the pulley olso find the shaded region
The length of the best that is with the contact of rim of the pulley is (5/18)π cm.
The shaded region is 10√5 - (5/18)π cm.
How to calculate length of belt in a pulley?To find the length of the belt that is in contact with the rim of the pulley, we need to find the length of the arc of the circle with radius 5 cm that is between the points O and P.
The circumference of a circle with radius 5 cm is 2πr = 10π cm. So the fraction of the circle between O and P is 10/360 = 1/36 of the total circumference. Therefore, the length of the arc OP is (1/36) x 10π = (5/18)π cm.
To find the shaded region, we need to subtract the length of the belt in contact with the pulley from the length of the belt pulled to point P.
The belt pulled to point P is the hypotenuse of a right triangle with legs 5 cm (the radius of the pulley) and 10 cm (the distance from the center of the pulley to point P). Using the Pythagorean theorem, we can find the length of the belt pulled to point P:
h² = 5² + 10²
h² = 125
h = √125 = 5√5 cm
So the length of the belt pulled to point P is 2(5√5) = 10√5 cm.
Therefore, the length of the shaded region is 10√5 - (5/18)π cm. This is the length of the part of the belt that is not in contact with the pulley.
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FH bisects ZEFG. Find the indicated
angle measures.
m/GFH=71°. Find m/EFH and
m/EFG.
m/EFH=
m/EFG =
m/EFH = 109° and m/EFG = 18°. Angles in a straight line sum to 180°. Since m/GFH is 71°, the remaining angle measures must add up to the remaining 109°. Therefore, m/EFH must be 109° and m/EFG must be 18°.
To find m/EFH and m/EFG, we need to use the fact that angles in a straight line sum to 180°. We can use this fact to work out the missing angle measures.
First, we note that m/GFH is 71°. This means that the remaining angles must add up to the remaining 109°.
We can then calculate m/EFH by subtracting m/GFH from 180°. m/EFH is therefore 180° - 71° = 109°.
Next, we can calculate m/EFG by subtracting m/EFH from 180°. m/EFG is therefore 180° - 109° = 18°.
Therefore, m/EFH = 109° and m/EFG = 18°.
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need assistance with my homework
Answer:
Step-by-step explana add
The triangle ABC id mapped onto triangle A' B'C' with vertices A'(3,1) , B'(1,-2) , C'(1,2)
Under the translation T= (2/3)Find the vertices of triangle ABC. (No need to draw).
Step-by-step explanation:
To find the vertices of triangle ABC after the translation T = (2/3), we can use the following formula:
(x', y') = (x + 2/3, y + 2/3)
where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the translated point.
Using this formula, we can translate each vertex of triangle A'B'C' back to its original position:
Vertex A:
x = 3 - 2/3 = 7/3
y = 1 - 2/3 = 1/3
Therefore, the coordinates of vertex A in triangle ABC are (7/3, 1/3).
Vertex B:
x = 1 - 2/3 = 1/3
y = -2 - 2/3 = -8/3
Therefore, the coordinates of vertex B in triangle ABC are (1/3, -8/3).
Vertex C:
x = 1 - 2/3 = 1/3
y = 2 - 2/3 = 4/3
Therefore, the coordinates of vertex C in triangle ABC are (1/3, 4/3).
Therefore, the vertices of triangle ABC are (7/3, 1/3), (1/3, -8/3), and (1/3, 4/3).
Answer:
Let A(x1, y1), B(x2, y2), and C(x3, y3) be the vertices of triangle ABC.
Under the translation T, each point (x, y) is mapped to the point (x + 2/3, y), which means that the new coordinates of A, B, and C will be:
A' = (x1 + 2/3, y1)
B' = (x2 + 2/3, y2)
C' = (x3 + 2/3, y3)
We are given the coordinates of A' (3, 1), B' (1, -2), and C' (1, 2), so we can set up a system of equations to solve for the coordinates of A, B, and C:
x1 + 2/3 = 3 => x1 = 2 1/3
y1 = 1
x2 + 2/3 = 1 => x2 = 1/3
y2 = -2
x3 + 2/3 = 1 => x3 = 1/3
y3 = 2
Therefore, the vertices of triangle ABC are A(2 1/3, 1), B(1/3, -2), and C(1/3, 2).
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56x^2 = 252x Solve using the quadratic formula
Answer:
x=0,[tex]\frac{9}{2}[/tex] Decimal Form: 0, 4.5
Step-by-step explanation:
1 )Move all terms to one side.
56[tex]x^{2}[/tex]-252x=0
2 )Factor out the common term 28x.
28x(2x−9)=0
3 )Solve for x
x=0,[tex]\frac{9}{2}[/tex] Decimal Form: 0, 4.5
Work out the value of f in the following equation:
f sin 42° = 2.5
Give your answer to 2 d.p.
Answer:
f = 3.74
Step-by-step explanation:
f sin 42° = 2.5
f = 2.5 (sin 42° = 0.669)
sin 41°
= 3.736
= 3.74 (2.d.p.)
The value of f in the given equation is 3.74.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is,
f sin 42° = 2.5
Dividing both sides of the equation by sin 42°,
f = 2.5 / sin 42°
f = 3.74
Hence the value of f is 3.74.
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the price of a cup of coffee has risen to $2.75 today. yesterday's price was $2.40. find the percentage increase. round your answer to the nearest tenth of a percent.
To find the percentage increase in price from yesterday's price to today's price, we can use the following formula:
Percentage Increase = ((New Value - Old Value) / Old Value) x 100
Plugging in the given values, we get:
Percentage Increase = ((2.75 - 2.40) / 2.40) x 100
Percentage Increase = (0.35 / 2.40) x 100
Percentage Increase = 0.1458 x 100
Percentage Increase = 14.58%
Therefore, the percentage increase in price from yesterday's price to today's price is 14.58%, rounded to the nearest tenth of a percent.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
The statement which most closely summarizes the data is that about 80 necklaces have more than 28 beads. The solution has been obtained by using the standard deviation.
What is standard deviation?
The standard deviation measures how skewed the data are with respect to the mean. Data are said to be more densely grouped around the mean and more dispersed, respectively, when the standard deviation is low and large.
We are given that the mean for the normal distribution is 24 beads and the standard deviation is 4 beads.
Now,
⇒ P (X ≥ 28) = 1 - P (X < 28)
⇒ P (X ≥ 28) = 1 - P ([tex]\frac{X-24}{4}[/tex] < 1)
⇒ P (X ≥ 28) = 1 - P (Z < 1)
⇒ P (X ≥ 28) = 1 - 0.84
⇒ P (X ≥ 28) = 0.16
Now, since the total necklaces are 500, the necklaces which have more than 28 beads are as follows:
⇒ 500 * 0.16
⇒ 80 necklaces
Hence, the third option is the correct answer.
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Question: The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
A )About 24 necklaces have more than 28 beads.
B )About 48 necklaces have more than 28 beads.
C)About 80 necklaces have more than 28 beads.
D)About 96 necklaces have more than 28 beads.
Which inequality is not true?
- 7/8 < -0. 60
- 7/8 > -0. 50
-7/8 > - 15/16
- 7/8 < - 1/4
7/8 is greater than -0.50, greater than -15/16, and less than -1/4. All of these inequalities are true except for 7/8 being less than -0.60.
To solve the inequality 7/8 < -0.60, we need to manipulate it to get it in the form of an equation. First, we can multiply both sides of the inequality by 8, to get 7 < -8(0.60). Next, we can distribute the negative sign on the right side to get 7 < -4.80. Finally, we can subtract 7 from both sides of the equation to get 0 < -4.80 - 7, which equals 0 < -11.80. This means that 7/8 is not less than -0.60, which is the answer to the inequality.
To confirm this answer, we can also solve the inequality 7/8 > -0.50. Again, we can multiply both sides of the inequality by 8 to get 7 > -8(0.50). We can then distribute the negative sign to get 7 > -4. Now, if we subtract 7 from both sides of the equation, we get 0 > -4 - 7, which equals 0 > -11. This means that 7/8 is indeed greater than -0.50.
To further confirm our answer, we can solve the inequality 7/8 > -15/16.
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A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 40 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 12 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 14 yards.
What is the area of the playground?
1,728 square yards
1,264 square yards
864 square yards
800 square yards
The area οf the playgrοund is 1264 square yards. Hence, οptiοn B is cοrrect.
What is the geοmetry?Geοmetry is a branch οf mathematics that deals with the study οf shapes, sizes, pοsitiοns, angles, and dimensiοns οf οbjects in space.
Tο find the area οf the playgrοund, we need tο divide it intο twο triangles and οne rectangle, and then find the area οf each and add them tοgether.
The rectangle has a length οf 12 yards and a width οf 20 yards, sο its area is:
40 x 20 = 800 square yards.
Area of Triangle 1 with base 40 yd and height 12 yd:
= 1/2 × 40 × 12
= 240 square yards.
Area of Triangle 2 with base (12 + 20) yd and height 14 yd:
= 1/2 × 32 × 14
= 224 square yards.
Adding all the areas:
= 800 + 240 + 224
= 1264 square yards.
Thus, the area of the playground is 1264 square yards. Hence, option B is correct.
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Complete question:
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
1,728 square yards
1,264 square yards
864 square yards
800 square yards
Adriana opened a savings account 3 years ago. The account earns 7% interest, compounded quarterly. If the current balance is $300.00, how much did she deposit initially?
Answer: 243.617
Step-by-step explanation:
300 = [tex]x[/tex] x (1 + 7/100/4)^(4 x 3)
300 = [tex]x[/tex] x (1.0175)^12
300 = [tex]x[/tex] x 1.231
[tex]x[/tex] = 300/1.231
[tex]x[/tex] = 243.617
suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 6 minutes. determine the probability that the child must wait at least 9 minutes on the bus on a given morning.
The probability that the child must wait at least 9 minutes on a given morning is approximately 0.2231.
Let X be the waiting time at the bus stop. We know that X is exponentially distributed with mean 6 minutes. Therefore, the probability density function (PDF) of X is given by:
f(x) = 1/6 * e^(-x/6) for x >= 0
To find the probability that the child must wait at least 9 minutes, we need to calculate the following probability:
P(X >= 9) = integral of f(x) from 9 to infinity
= integral from 9 to infinity of (1/6 * e^(-x/6)) dx
Using integration by substitution, let u = x/6, du = 1/6 dx, so that:
P(X >= 9) = integral from 3/2 to infinity of e^(-u) du
= [e^(-u)] evaluated from 3/2 to infinity
= e^(-3/2)
≈ 0.2231
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2. For the table, identify the independent and dependent variables. Explain the relationship using words, and an equation (equation example: C = 2s + 20). Number of Snacks Purchased, "s" 1 2 3 Total Cost, $18 $21 $24 $27
The independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$". The relationship is linear, with $ = 3s + 15.
What is rate?A rate is a measure of the amount of change of one quantity with respect to another quantity, often expressed as a ratio or a fraction. It tells us how much one quantity changes per unit of time or per unit of another quantity. Examples of rates include speed, velocity, acceleration, interest rate, and growth rate
According to the given information:In the given table, the independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$".
The relationship between the number of snacks purchased and the total cost is a linear relationship, where the total cost increases by $3 for every additional snack purchased.
We can write the equation for the relationship between the two variables as:
$ = 3s + 15
Here, the constant term 15 represents the fixed cost or the cost of buying zero snacks. The coefficient 3 of the independent variable "s" represents the additional cost incurred for each additional snack purchased.
Therefore, The independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$". The relationship is linear, with $ = 3s + 15.
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solve the inequality 4x-7<5
Answer:
x < 3
Step-by-step explanation:
4x -7 < 5
4x < 12
x < 3
Answer:x < 3
Step-by-step explanation:4x -7 < 5
4x < 12
x < 3
6(2x – 1) – 12 = 3(7x + 4)
a.-18
b.9
c.18
Answer:
x = -10/3
Step-by-step explanation:
6(2x – 1) – 12 = 3(7x + 4)
12x - 6 - 12 = 21x + 12
12x - 18 = 21x + 12
-9x - 18 = 12
-9x = 30
x = -30/9
x = -10/3
Answer:
Step-by-step explanation:
[tex]6(2x -1) - 12 = 3(7x + 4)[/tex]
[tex]12x-6-12=21x+12[/tex] (multiplied to remove brackets)
[tex]12x-18=21x+12[/tex]
[tex]12x=21x+30[/tex] (+18 to both sides of the equation)
[tex]-9x=30[/tex] (-21x both sides)
[tex]x=-\frac{30}{9}=-\frac{10}{3}[/tex] (÷-9 both sides and then simplified the
fraction)
None of the answers are correct
Find x and y . I don’t understand. Math help plsssss
Answer:
x = y = 5
Step-by-step explanation:
This triangle and its markings show that the acute angles are equal. Given that it is a right triangle, this is a 45-45-90 triangle. This also means that the values of x and y are equal. Note that for any triangle, if two angles are equal, then their corresponding side lengths are also equal. The side lengths for this type of triangle follow the pattern s - s - s√2 where the first two are side lengths and last value is the length of the hypotenuse. (s represents the length of a side)
We want to find x and y, so we need the value of s.
s√2 = 5√2
s = 5
Therefore, x = 5, y = 5.
Consider the following 7 natural numbers: 6,8,11, 16, 19, 22, 23. a) Three of these numbers can be decomposed in the form 2. A + 1, where A is another natural number. Which three numbers can be written in this form? Show your work. b) In one sentence, identify what the numbers in part a) have in common.
I need help with this! Someone explain please
a) The numbers that can be decomposed in the form 2A + 1 are the ones that are odd when subtracted by 1 and then divided by 2. So, we can check each number to see if it satisfies this condition:
6: (6 - 1)/2 = 2.5 (not a natural number)
8: (8 - 1)/2 = 3.5 (not a natural number)
11: (11 - 1)/2 = 5
16: (16 - 1)/2 = 7.5 (not a natural number)
19: (19 - 1)/2 = 9
22: (22 - 1)/2 = 10.5 (not a natural number)
23: (23 - 1)/2 = 11
So, the three numbers that can be decomposed in the form 2A + 1 are 11, 19, and 23.
b) The numbers in part a) have in common that they are odd.
Hey can you please help me
Answer:
Step-by-step explanation:
Mason subtracted 5 from each side instead of adding 5.
x - 5 < 11
x - 5 + 5 < 11 + 5
x < 16
The number line will have an open circle at 16 since it does not include
16. It will be shaded to the left from that open circle as it includes
all values less than 16.
The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.T/F
The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct
The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.
Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.
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consider the sample of 1,400 past negligence cases. suppose you are willing to let the 67% estimate be within .025 (2.5%) of the true proportion. you are willing to assume a 95% confidence. a. is 1,400 an adequate sample size for the estimate of 67%? show why or why not\
We can be reasonably confident that our estimate adequate sample size of 67% is within 2.5% of the true proportion.
To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.
We can use the following formula to calculate the margin of error:
[tex]E = z \sqrt{\frac{(p (1-p)}{n} )[/tex]
where:
E is the margin of errorz is the z-score corresponding to the desired confidence level (95% corresponds to a z-score of 1.96)p is the estimated proportion (67% or 0.67 as a decimal)n is the sample size (1,400)Plugging in the values, we get:
[tex]E = 1.96 \sqrt{(0.67 (1-0.67)/1400)[/tex]
≈ 0.025
Thus, the error margin is around 0.025. This indicates that there is a 95% chance that the real percentage will be within 0.025 of the estimated proportion.
We may infer that a sample size of 1,400 is sufficient for predicting a proportion of 67% with the provided degree of confidence and tolerance as the computed margin of error is equal to the required tolerance level. As a result, we can say with some degree of assurance that our estimate of 67% is within 2.5% of the actual proportion.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 45 , 15 , 5 , . . . 45,15,5,...
Answer: Geometric and common difference is 1/3
Step-by-step explanation:
what is the rate of change between 75 and 125 miles driven
The rate of change between 75 and 125 miles is calculated by dividing the difference between the fuel cost at 125 and 75 miles by the distance traveled. The fuel cost at 75 miles is $3.85, while the fuel cost at 125 is $6.35. The rate of change is $0.05 per mile.
What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?To calculate the rate of change between 75 and 125 miles, subtract the fuel cost at 125 miles from the fuel cost at 75 miles and divide the difference by the distance travelled:
Rate of change = (fuel cost at 125 miles - fuel cost at 75 miles) / (125 - 75)
First, we need to find the fuel cost at 75 miles:
() = 0.1 + 0.05x
() = 0.1 + 0.05(75)
() = 3.85
The fuel cost at 75 miles is $3.85.
Next, we need to find the fuel cost at 125 miles:
() = 0.1 + 0.05x
() = 0.1 + 0.05(125)
() = 6.35
The fuel cost at 125 miles is $6.35.
Now we can substitute these values into the rate of change formula:
Rate of change = (6.35 - 3.85) / (125 - 75)
Rate of change = 2.5 / 50
Rate of change = 0.05
The rate of change of the cost of fuel when the car travels from 75 miles to 125 miles is $0.05 per mile.
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The complete question is: If a car travels x miles, the cost of fuel used is given by the function () = 0.1 + 0.05x dollars. What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?
a bookstore took an inventory of the prices of its books and created a histogram to show the results. what shape does the distribution have?
The required shape of the attached histogram of the prices of the books is given as bell shaped.
General characteristics of histograms ,based on some general observations are,
If the histogram is roughly symmetric around its center, then the distribution is likely to be approximately normal (bell-shaped).
If the histogram has a peak on one side and a long tail on the other, then the distribution is likely to be skewed (either positively or negatively skewed).
If the histogram has multiple peaks or modes, then the distribution is likely to be multimodal.
Based on these observations,
The shape of the distribution in the bookstore's inventory is bell shaped.
As here in the attached histogram is symmetric around its center.
It is almost symmetric between 100 to 150 dollars.
Therefore, the shape of the distribution of the prices of books is bell shaped in the attached histogram.
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The above question is incomplete, the complete question is:
A bookstore took an inventory of the prices of its books and created a histogram to show the results. what shape does the distribution have?
Diagram is attached.
Sheila is searching career possibilities. She found that an actuary requires a bachelor's degree in
mathematics or statistics. The median salary is $94,740 a year in some parts of the country. She
also found that a nuras practitioner requires a Bachelor's degree in nursing and a master's or doctorate
in nursing. The median salary is $89.960 a year. In 20 years, how much more would an actuary earn
than a nurse practitioner?
A $1,894,800
8 $95,600
C $4,780
D $1,799,200
Step-by-step explanation:
Based on the information you provided, an actuary earns $94,740 per year while a nurse practitioner earns $89,960 per year. The difference in their annual salaries is $4,780. Over 20 years, an actuary would earn $95,600 more than a nurse practitioner (20 years * $4,780/year = $95,600).
f(x)=3 squared root x + 11. Find the inverse of f(x)
Answer:
[tex] \frac{x {}^{2} }{9} - 11[/tex]
50 PTS!! only right answers pls!!
yesterday there were b junebugs. today there are [tex]b^{2}[/tex]
junebugs. how many where there yesterday?
Answer:
Step-by-step explanationThere are more than 800 species of June bugs known to science and more are discovered every year. Adult beetles are usually blackish or reddish brown in colour, and tend to be very hairy on their fronts: