The radius of the sphere when the volume and the radius are increasing at the same numerical rate is √(1/2π) cm.
The numerical rate of increase in the volume of a sphere with respect to the increase in the radius is given by numerical rate,
dn/dt=4πr² * dr/dt.
Here, dn/dt is the rate of increase of volume with time, dr/dt is the rate of increase of radius with time, and r is the radius of the sphere.
The rate of increase of radius is given as dr/dt=18 cm/s. We need to find the radius of the sphere when the volume and the radius are increasing at the same numerical rate.
Let dn/dt=18 cm³/s, which means the volume and radius are increasing at the same numerical rate. Then
18=4πr² * 18So, r²=1/2π => r = √(1/2π) cm
Therefore, In a sphere whose volume and radius increase at the same numerical rate, the radius is √(1/2π) cm.
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myas rectangular yard is 10 feet wide and 15 feet long. how many square feet of grass does she need to plant if she wants to cover the entire yard?
ANSWER FASTTTTT
To cover the entire yard, Mya needs to plant 150 square feet of grass.
Mya's rectangular yard is 10 feet wide and 15 feet long. To find the area of the yard, we need to multiply the width by the length:
Area of yard
= width x length
= 10 ft x 15 ft
= 150 square feet
Therefore, Mya needs to plant 150 square feet of grass to cover the entire yard
A rectangular yard is a type of outdoor space that is often used for gardening, outdoor activities, or as a place for relaxation. To calculate the area of a rectangular yard, you need to know its dimensions, which are typically expressed in feet or meters. The area of a rectangular yard can be found by multiplying its length by its width. The formula for the area of a rectangle is A = L x W, where A represents the area, L represents the length, and W represents the width. Once you have calculated the area of the yard, you can use this information to determine how much grass or other landscaping materials you need to cover the area.
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1. A car's speed increases as it merges onto a highway. The car travels at 65 mph on the highway until it slows to exit. The car then stops at three traffic lights before reaching its destination. Draw a sketch of a graph that shows the car's speed over time.
Just make a flat line for each time the car stops.
Hope this helps.
0.5 ( 5 − 7 x ) = 8 − ( 4 x + 6 )
Answer:
Well,
[tex]0.5(5-7x)=8-(4x+6)\\-3.5x+2.5=-4x+2\\0.5x+2.5=2\\0.5x=-0.5\\x=-1[/tex]
Step-by-step explanation:
Hope this helps!^^
Answer: -1
Step-by-step explanation:
first you want to simplify 0.5 (5-7x) which will get you 2.5 - 3.5x
then you will do the same for the other side move the xs to one side then treat it like any other problem
Paul gets $5 every week for doing his chores. He is saving his money to buy a skatboard that costs $85. He has already saved $25. A : w = 85 / 5
B : w = 85 - 25
C : w - 85 / 5 - 25
D: w = 85-25/ 5
The answer is D: w = 85-25/ 5. This equation represents the number of weeks it will take Paul to save enough money to buy the skateboard.
What is equation?Equations are useful for solving problems, finding unknown values, determining rates of change, and understanding relationships between different variables.
The equation can be written as w = (85 - 25)/5, where 85 is the cost of the skateboard, 25 is the amount he has already saved, and 5 is the Subtracting 85-25, the equation is essentially asking how many 5s are in 60.
The answer is 12, which is the number of weeks it will take Paul to save enough money for the skateboard.
This can be verified by multiplying 12 by 5, which equals 60.
Thus, the correct answer is D: w = 85-25/ 5.
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Question :
Paul gets $5 every week for doing his chores. He is saving his money to buy a skateboard that costs $85. He has already saved $25. Which equation describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard?
A : w = 85 / 5
B : w = 85 - 25
C : w - 85 / 5 - 25
D: w = 85-25/ 5
I need help with the last one which is prove AB and CD.
Answer:
because triangle ABD is congruent to triangle CBD
by CPCT
AB = CD
If a porch is 12 cm by 19 cm what is the area of the point?
the area of the porch is 228 square centimeters. To calculate the area of a porch, we need to use the formula for the area of a rectangle, which is:
Area = length x width
In this case, the length of the porch is 19 cm and the width is 12 cm. So, we can plug these values into the formula:
Area = 19 cm x 12 cm
Area = 228 cm^2
Therefore, the area of the porch is 228 square centimeters.
It's important to note that when we use the term "area," we are referring to the amount of space that is enclosed within the boundaries of the porch. In other words, we are calculating the size of the surface area of the porch, which is measured in square units.
Knowing the area of a porch can be useful in a variety of contexts. For example, if you were planning to install new flooring on the porch, you would need to know the area in order to calculate how much material you would need to purchase. Similarly, if you were planning to paint the porch, you would need to know the area in order to estimate how much paint you would need to cover the surface.
In summary, the area of a porch can be calculated by multiplying its length and width, and is measured in square units.
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f(x) = 16, x = *
f(x) = x² - 6x + 9
Multiple choice: Finding: x values
-7
7
1
-1
The values of the variable x are 7 and -1. Options B and D
What are functions?
Functions are simply defined as those equations, expressions or laws that shows the relationship between two variables.
These variables are;
The independent variablesThe dependent variablesFrom the information given, we have that;
f(x) = 16
f(x) = x² - 6x + 9
Now, equate the two functions, we have;
x² - 6x + 9 = 16
collect the like terms
x² - 6x + 9 - 16 = 0
subtract the values
x² - 6x - 7 = 0
solve the quadratic equation
x² - 7x + x - 7 = 0
x(x - 7) + 1( x - 7)
Then, x = 7 and -1
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For each of the shapes below, state whether it is a regular polygon, an irregular
polygon or neither.
A
D
B
E
C
Each of the shapes below, The polygons are identified as:
A- Irregular polygon
B- Neither
C- Regular polygon
D- Regular polygon
E- Regular polygon
What is polygon?A polygon is a two-dimensional geometric shape that is defined as a closed figure with three or more straight sides and angles. Polygons can be convex or concave, depending on whether all of their interior angles are less than or greater than 180 degrees, respectively. Some common examples of polygons include triangles (3 sides), squares (4 sides), pentagons (5 sides), hexagons (6 sides), and octagons (8 sides). Polygons are frequently used in geometry, as they can be used to calculate areas, perimeters, and other properties of shapes.
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Addison wanted to know if there was a connection between her coffee consumption and how
well she slept that night. For weeks, Addison recorded how many cups of coffee she drank in
the morning and how many hours she slept that night.
0 cups of coffee
1 cup of coffee
6 hours 7 hours
1
5
5
4
What is the probability that a randomly selected day is one when she drank exactly 1 cup of
coffee and is one when she slept about 6 hours?
Simplify any fractions.
Answer:
Step-by-step explanation:
Find dy/dx for y=4sin²(3x)
Answer:
24 sin(3x) cos(3x)
Step-by-step explanation:
To find:-
The derivative of y = 4sin²(3x) .Answer:-
The given function to us is ,
[tex]:\sf\implies y = 4sin^2(3x) \\[/tex]
To find it's derivative we would have to use Chain rule of differentiation , which is ;
[tex]:\sf\implies \pink{ \dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}} \\[/tex]
Taking the given function,
[tex]:\sf\implies y = 4sin^2(3x) \\[/tex]
Differentiate both sides with respect to x,
[tex]:\sf\implies \dfrac{dy}{dx}=\dfrac{d}{dx}4sin^2(3x)\\[/tex]
We can take out the constant as ,
[tex]:\sf\implies \dfrac{dy}{dx}= 4 \dfrac{d}{dx}sin^2(3x) \\[/tex]
Multiply and divide by sin(3x) as ,
[tex]:\sf\implies \dfrac{dy}{dx}= 4 \bigg( \dfrac{d(sin^23x)}{d(sin3x)}\times \dfrac{d\ sin3x}{dx}\bigg)\\[/tex]
Differentiation of sin(nx) is n cos(nx) and
[tex]:\sf\implies \pink{ \dfrac{d(x^n)}{dx} = nx^{n-1} }[/tex]
So that ,
[tex]:\sf\implies \dfrac{dy}{dx}= 4 ( 2sin(3x) \cdot 3cos(3x))\\[/tex]
Simplify,
[tex]:\sf\implies\pink{ \dfrac{dy}{dx}= 24\ sin(3x) \ cos (3x)}\\[/tex]
Hence the derivative of the given function is 24 sin(3x) cos(3x) .
[tex]\rule{200}2[/tex]
Related formulae :-
[tex]\boxed{\boxed{\begin{minipage}{5cm}\displaystyle\circ\sf\;\dfrac{d}{dx}(sin\;x)=cosx \\\\ \circ \;\dfrac{d}{dx}(cos\;x) = -sinx \\\\ \circ \; \dfrac{d}{dx}(tan\;x) = sec^{2}x \\\\ \circ\; \dfrac{d}{dx}(cot\;x) = -csc^{2}x \\\\ \circ \; \dfrac{d}{dx}(sec\;x) = secx \cdot tanx \\\\ \circ \; \dfrac{d}{dx}(csc\;x) = -cscx \cdot cotx \\\\ \circ\; \dfrac{d}{dx}(sinh\;x)=coshx \\\\ \circ\; \dfrac{d}{dx}(cosh\;x)= sinhx \\\\ \circ\;\dfrac{d}{dx}(tanh\;x)=sech^{2}h \\\\ \circ\;\dfrac{d}{dx}(coth\;x)=-csch^{2}x \\\\ \circ\;\dfrac{d}{dx}(sech\;x) =-sechx \cdot tanhx \\\\ \circ\;\dfrac{d}{dx}(csch\;x) = -cschx \cdot cothx\end{minipage}}}[/tex]
[tex]\rule{200}2[/tex]
Answer:
[tex]\dfrac{\text{d}y}{\text{d}x}=12 \sin (6x)[/tex]
Step-by-step explanation:
To find the derivative of y = 4sin²(3x), use the chain rule.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
The given function can be written as:
[tex]y=4(\sin 3x)^2[/tex]
Let y = 4u², where u = sin(3x).
Differentiate the two parts separately.
[tex]\dfrac{\text{d}y}{\text{d}u}=8u \quad \text{and} \quad \dfrac{\text{d}u}{\text{d}x}=3 \cos (3x)[/tex]
Put everything into the chain rule formula:
[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x}& =\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}\\\\&=8u \times 3 \cos (3x)\\\\&=24u \cos (3x)\\\\&=24 \sin (3x) \cos (3x) \end{aligned}[/tex]
Simplify using the sine double angle identity:
[tex]\boxed{\sin (2 \theta)= 2 \sin \theta \cos \theta}[/tex]
[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x}&=24 \sin (3x) \cos (3x) \\\\&=12(2 \sin (3x) \cos (3x))\\\\&=12 \sin (2 \cdot 3x)\\\\&=12 \sin (6x)\end{aligned}[/tex]
Therefore:
[tex]\dfrac{\text{d}y}{\text{d}x}=12 \sin (6x)[/tex]
[tex]\hrulefill[/tex]
Differentiation Rules[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Differentiating $\sin (ax)$}\\\\If $y=\sin(ax)$, then $\dfrac{\text{d}y}{\text{d}x}=a \cos (ax)$\\\end{minipage}}[/tex]
When driving in normal conditions on a rural roadway your following distance should bea) no more than one secondb) three secondsc) twelve secondsd) four seconds or more
When driving in normal conditions on a rural roadway, your following distance should be four seconds or more because it gives you more time to respond to any unexpected occurrences that might occur. therefore option d) four seconds or more is correct.
What is a following distance?Following distance is the amount of space between a car and the car in front of it when driving on the road. It's essential to keep a safe following distance because it gives you more time to react if the car in front of you makes a sudden stop or starts to slow down. It's critical to keep a safe following distance because it's not always possible to avoid sudden stops or slow-downs.
What is a rural roadway?A rural roadway is a road that runs through the countryside. In comparison to city roads, rural roads are less congested, with less traffic and less likelihood of accidents. As a result, it's essential to maintain a safe following distance when driving on rural roads because they're often long and wide, with higher speed limits and less congestion than city roads.
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Directions: Rewrite each expression using positive exponents.
1. X-5
2. 3m-2
3. -7a-4b3
4. 9x6y-3
Answer:
1) X0=1
2) 19m2
3) there is something missing i think
4) 6x3y
can someone please help
Answer:
The circle x^2+y^2-2x-8y+17=0 has translated 5 units to the leftand 2units down.
Step-by-step explanation:
If we translate this circle to the left 5 units, and 2 units down,
we will subtract 5 from the center x coordinate and 2 for the center y coordinate
The center is (1,-4)
So the new center prime is (-4,-6)
Since a translation keep angles and measures,
Our radius will remain untouched so our new equation is
[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]
[tex]\sqrt{ 6^{2} +(x-2)^{2} }[/tex]
Answer:
[tex] \sqrt{36 + x {}^{2} } - (2) {}^{2} \\ 6 + x + - 2 \\ 6 - 2 + x \\ 4 + x \\ \: \:answer = 4 + x \\[/tex]
The vertices of a rectangle are plotted.
A graph with both the x and y axes starting at negative 7, with tick marks every one unit up to 7. The points negative 4 comma 2, 5 comma 2, 5 comma negative 3, and negative 4 comma negative 3 are each labeled.
What is the perimeter of the rectangle?
10 units
18 units
28 units
45 units
Answer:
Answer is 28
Step-by-step explanation:
Length = 5
Width = 9
Perimeter = length*2 + width*2
Perimeter = 5*2 + 9*2
Perimeter = 10 + 18 = 28
write a polynomial to represent the volume of the rectangular prism if 0.5x-3 and x-4 and x+5
The polynomial to represent the volume of the rectangular prism is:
V = (0.5x - 3) × (x - 4) × (x + 5)
Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60
How to calculate the volume (V) of a rectangular prism?
The volume (V) of a rectangular prism can be calculated using the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism respectively.
Here, the length (l) can be represented by (0.5x - 3), the width (w) can be represented by (x - 4), and the height (h) can be represented by (x + 5).
Therefore, the polynomial to represent the volume of the rectangular prism is:
V = (0.5x - 3) × (x - 4) × (x + 5)
Simplifying this expression gives V = 0.5x³ - 6.5x² - 23x + 60
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Lee Ann bought 2 cartons of yogurt. She ate 1 over 8 of a carton of yogurt each dat. How many days did it take Lee Ann to eat all of the yogurt in the 2 cartons?
This problem can be solved by the unitary method. If Lee Ann bought 2 cartons of yoghurt, she would take 16 days to finish two cartoons as there were 8 yoghurt in each cartoon.
The unitary method involves first determining the value of a single unit, followed by the value of the necessary number of units.
Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. In the aforementioned issue, the number of apples is known, but it is unclear what they are worth. It should be noted that issues with this method are solved using the concepts of ratio and proportion.
Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when applying the unitary method to a problem.
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PLSS ANSWER QUICK
Based on the line of best fit, what is the expected distance Bobby has traveled after 8 hours?
A.475 miles
B. 300 miles
C. 400 miles
D. 500 miles
Answer: 475 is ur answer
Step-by-step explanation:
if two different students are randomly selected (i.e., without replacement), find the probability that both the first and second student studied.
The probability that both the first and second student studied = p²
To find the probability that both the first and second students studied when two different students are randomly selected, we can use the multiplication rule of probability.
What is the multiplication rule of probability?The multiplication rule of probability states that if the probability of event A is p(A), and the probability of event B, given that event A has occurred, is p(B|A), then the probability of the joint occurrence of A and B is given by p(A and B) = p(A) × p(B|A).
So, if we let A be the event that the first student studied, and B be the event that the second student studied, then we need to find the probability of the joint occurrence of A and B.
We can assume that the probability that any student studied is equal to some value p, and the probability that any student didn't study is equal to q = 1 - p. Since there are only two possibilities for each student (studied or not studied), then p + q = 1. So, we can use the complement rule of probability to write:
p(A) = probability that the first student studied = p, and
p(not A) = probability that the first student didn't study = q = 1 - p,
p(B|A) = probability that the second student studied, given that the first student studied = p, and
p(B|not A) = probability that the second student studied, given that the first student didn't study = p.To find the probability that both the first and second student studied, we need to find the probability of the joint occurrence of A and B. Using the multiplication rule, we get:
p(A and B) = p(A) × p(B|A) = p × p = p².
Which is the probability that both the first and second students studied.
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Solve the system of linear equations by elimination. -x+y=1 and 3x+y=7
We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.
3x + y = 7
-x + y = 1
Add the equations together:
2x + 2y = 8
Divide both sides by 2:
x + y = 4
Subtract the second equation from the first:
-x + y = 1
x - y = -3
Add the equations together:
2x = -2
Divide both sides by 2:
x = -1
Substitute -1 for x in the equation x + y = 4:
-1 + y = 4
Subtract -1 from both sides:
y = 5
The solution is x = -1 and y = 5.
We begin by solving the system of linear equations by elimination. We need to get the variables to one side of the equation and the constants to the other side. We start by adding the two equations together: 3x + y = 7 and -x + y = 1. This gives us 2x + 2y = 8, which we can then divide both sides by 2 to get x + y = 4. We then subtract the second equation from the first to get -x + y = 1 and x - y = -3. We then add these two equations together to get 2x = -2 and divide both sides by 2 to get x = -1. We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.
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What are the steps in the design process, and how are they organized in Architecture?
These steps in the design process are often iterative, meaning that architects may revisit earlier steps as they refine and develop the design. The overall goal of the design process in architecture is to create a functional, safe, and aesthetically pleasing building that meets the needs and goals of the client.
What are the steps in the design process?The following are the steps in the design process, organized in architecture:
Programming: In this first step, architects work with their clients to understand the project requirements, goals, and objectives. They may gather information about the site, zoning and building codes, budget, and other constraints.
Schematic Design: In this step, architects use the information from the programming phase to create rough sketches and drawings that show the basic layout and massing of the building. This phase is an opportunity to explore various design options and to get feedback from the client.
Design Development: In this step, the architects refine the design, incorporating structural and mechanical systems, and developing detailed drawings and specifications. This phase also includes working with consultants such as engineers and contractors.
Construction Documents: In this step, the architects prepare the final construction documents, which include detailed drawings and specifications that will be used by contractors to build the project.
Bidding and Negotiation: In this step, the architects help the client solicit bids from contractors and negotiate the terms of the construction contract.
Construction Administration: In this final step, the architects oversee the construction process, ensuring that the project is built according to the design documents and that any changes or issues are addressed.
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Lauri spent 5% of x hours at her part-time job. What is x if 5% of x is about 10 hours? Explain how you estimated and which property of equality you used to find x.
To estimate x, we can use the fact that 5% is approximately equal to 1/20. Therefore, if 5% of x is about 10 hours, then we can estimate that 1/20 of x is also about 10 hours.
Multiplying both sides of the equation 1/20 x = 10 by 20, we get x = 200.
To check our answer, we can verify that 5% of 200 hours is indeed about 10 hours.
We used the multiplication property of equality to solve for x, which states that we can multiply both sides of an equation by the same non-zero number without changing the solution. In this case, we multiplied both sides by 20.
Work out he area of this circle. Take pi to be 3. 142 and give your answer to 1 decimal place
The area of circle with radius 4 centimetres and the special math constant, pi to be 3. 142 is equals to the 50.3 cm².
Area of a shape is defined as the total spece covered by shape in two-dimensional. In geometry, the area enclosed circle is calculated by π times the square of radius of circle. Formula of Area = π × r², where 'r' is the radius. The units of area are square of units of radius that if radius in feet then unit of area will be square feet. We have a circle with radius say r = 4 cm.
The value of specific math constant, pi ( i.e., π) is equals to be 3.142. We have to determine the area of circle. The area of circle, A = π× 4²
=> A = 16π
=> A = 16× 3.142
=> A = 50.272 ~ 50.3 cm²
Hence, the required area value is 50.3 cm².
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Complete question:
The above figure completes the question.
Work out he area of this circle. Take pi to be 3. 142 and give your answer to 1 decimal place
A line is drawn on a coordinate grid by the equation y = 1. Which of the following lines would represent a row perpendicular to it?
Among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.
What is coordinate geometry?
Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric figures using coordinates.
The line y = 1 is a horizontal line that goes through all points on the y-axis with a y-coordinate of 1.
To find a line perpendicular to it, we need to find a line that has a slope that is the negative reciprocal of the slope of y = 1. The slope of y = 1 is 0, so the slope of the perpendicular line is undefined (since any number divided by 0 is undefined).
Therefore, the perpendicular line must be a vertical line, and its equation would be of the form x = c, where c is a constant.
Hence, among the answer choices, the line that represents a row perpendicular to y = 1 is x = 4.
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Can someone please help me? I’ll give brianliest!
Answer:
B
Step-by-step explanation:
first you would need to do the inverse of sine to get the angle since normal sine would give you the length and you need the angle.
An easy way to remeber sine, cosine and tangent is
SOH CAH TOA
sin= opposite/ hypotenuse
cosine= adjacent/ hypotenuse
tangent= opposite/adjacent.
first label your triangle with the sides hypotenuse, adjacent and opposite.
hypotenuse is the longest side that is diagonal in this case like ab
opposite is the side that is opposite the angle you are looking for, so in thsi case line cb
adjacent is the like next to the angle you are trying to find so in thsi case like ac
and since we know sine inverse = opposite/hypotenuse = angle
(we are using sine for this question since that is what the question is asking for)
we simply do
sine inverse= 3/5
so the answer is B
i hope this helps! :)
Answer:B
Step-by-step explanation: im sure because i answer that in school im correct
The digits of a two-digit number sum to 11 and have a positive difference of 1. Which of these MUST be true?
a. The product of the digits of the two-digit number is 30.
b. The two-digit number is a multiple of 5.
c. The two-digit number is even.
d. The two-digit number is 83.
Answethe two digit is a multiple of 5
Step-by-step explanation:
the two-digit number is 65 so, options that must be true are a and b.
Define additionAddition is a basic arithmetic operation that combines two or more numbers to produce a sum or total
Let x stand for the tens digit and y for the units digit.
x + y = 11 (the digits of the two-digit number sum to 11)
x - y = 1 (the positive difference of the digits is 1)
Adding these two equations gives:
2x = 12
So x = 6.
Substituting x = 6 into either of the equations gives y = 5.
Therefore, the two-digit number is 65.
Now we can check which of the options is true:
a. The two-digit number has a product of 30 digits.
6 x 5 = 30, so this is true.
b. The number has two digits and is a multiple of 5.65 is a multiple of 5, so this is true.
c. The two-digit number is even.
65 is not even, so this is false.
d. The two-digit number is 83.
The two-digit number is 65, not 83, so this is false.
Therefore, the options that must be true are a and b.
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what two numbers do you multiply to get 18 and add to get -11
Answer:
-9 and -2
Step-by-step explanation:
-9 and -2
two negatives multiply to make a positive (18)
and -9 add -2 is -11
A researcher looking for evidence of extrasensory perception (ESP) tests 1000 1000 subjects. Nine of these subjects do significantly better ( P < 0.01 ) (P<0.01) than random guessing.
(a) Nine subjects may seem like a lot of people, but can you conclude that these nine people have ESP? Select the appropriate statement that explains whether or not it is proper to conclude that these nine people have ESP.
Yes. This follows directly from the 1 % 1% significance level.
Yes. This follows directly from the statistical significance.
No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.
No. The sample size was not large enough for any statistical inference.
it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.
No. Since the tests were performed at the 1% significance level, as many as 10 subjects may have done significantly better than random guessing.
When conducting hypothesis testing, the significance level (in this case, 0.01 or 1%) is the probability of rejecting the null hypothesis when it is actually true. This means that there is a 1% chance of observing a significant result purely by chance, even if the null hypothesis (in this case, that the subjects do not have ESP) is true.
In this scenario, nine subjects performed significantly better than random guessing, which may suggest that they have ESP. However, due to the possibility of observing significant results by chance, it is not proper to conclude that these nine people have ESP. There is still a chance that these results are purely coincidental.
Additionally, it is important to note that the sample size of 1000 subjects is large enough for statistical inference, but the significance level must be taken into account when interpreting the results.
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Given triangle ABC with points:
A - (1, -3)
B - (3, 0)
C - (4, -2)
Rotate ABC 90 degrees counterclockwise about the origin then reflect it over the x-axis. Determine the ordered pairs for A', B', and C'.
The points A', B', and C' are (3, 1), (0, 3) and (-2, 4) respectively. The solution has been obtained by using the concept of transformation.
What is transformation?
Transformations allow for the translation, rotation, and reflection of shapes on a coordinate plane. Any line, point, or vector can be rotated, translated, or reflected.
We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).
Now, we need to rotate the triangle ABC 90 degrees about the origin.
We know that the rotation rule for rotating 90 degrees about the origin is that (x, y) becomes (y, -x).
So, from this we get the coordinates as
A' (3, -1)
B' (0, -3)
C' (-2, -4)
Now, on reflecting it over the x - axis, we get
A' (3, 1)
B' (0, 3)
C' (-2, 4)
Hence, the points A', B', and C' are (3, 1), (0, 3) and (-2, 4) respectively.
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please does anyone know how to solve this table
Assuming the table models a linear equation, we will get the complete table:
minutes: 10 40 89.3 150 360
cost: 200 225.7 268 320 500
How to complete the table?Here we can assume that the table models a linear equation of the form:
y = ax+ b
Where a is the rate of change and b is the y-intercept.
If we know two points on the line, let's say:
(x₁, y₁) and (x₂, y₂), then the rate of change is:
a = (y₂ - y₁)/(x₂ - x₁)
In the table we have two pairs:
(10, 200) and (150, 320)
Then the rate is:
a = (320 - 200)/(150 - 10)
a = 12/14 = 6/7
Then we can write:
y = (6/7)*x + b
To find the value of b, we can replace one of the two points there, using (10, 200) we will get:
200 = (6/7)*10 + b
200 = 60/7 + b
200 - 60/7 = b
1400/7 - 60/7 = b
1340/7 = b
Then the line is:
y = (6/7)*x + 1340/7
Now to complete the table, just replace the correspondent values in the equation.
for the first value we have x = 40
y = (6/7)*40 + 1340/7 = 225.7
if x = 360
y = (6/7)*360 + 1340/7 = 500
if y = 268
268 = (6/7)*x + 1340/7
x = (268 - 1340/7)*(7/6)
x = 89.3
Then the complete table is:
minutes: 10 40 89.3 150 360
cost: 200 225.7 268 320 500
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