a mathematics professor created a test that was supposed to be mostly easy except for two challenging problems. the scores of the students are shown in the dot plot below. what was the highest grade? a dot plot has a horizontal axis labeled test score percentage from 70 to 100 in increments of 5. columns of dots are plotted over horizontal coordinates with heights as follows, where the horizontal coordinate is listed first and the number of dots in the column is listed second: 70, 1; 71, 1; 74, 1; 75, 2; 76, 2; 77, 3; 78, 2; 79, 4; 80, 5; 81, 5; 82, 6; 83, 7; 84, 7; 85, 9; 86, 11; 87, 13; 88, 14; 89, 15; 90, 14; 91, 13; 92, 2; 93, 2. do not include a percent symbol with your answer.

She had filled 88 spray pint bottles.

Given is that Ms. Wu runs a house cleaning business. To save money, she bought a 1 gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1 - pint spray bottles as she could.

1 pint = 0.125 gallons

Total amount = 11 gallons.

The total number of bottles that can be filled are -

n = 11/0.125

n = 88

Therefore, she had filled 88 spray pint bottles.

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On applying the supplementary angle rule, the value for x is obtained as 10°, and the angle 7x° is obtained as 70°.

What is a supplementary angle?

The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.

The line segment is given which has a ray diving the line segment.

Since it is a straight line, the total angle on it will be 180°.

The two angles given are 110° and 7x°.

Apply the supplementary angle rule =

On a straight line sum of two angles = 180°

Substitute the values in the equation -

110° + 7x° = 180°

Collect the like terms -

7x° = 180° - 110°

Apply the arithmetic operation of subtraction -

7x° = 70°

Apply the arithmetic operation of division -

x = 70/7

x = 10°

Now the angle 7x° = 7(10°) = 70°

Therefore, the angle value is obtained as 70°.

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From the given figure, equation represents the Pythagorean theorem is 13²=12²+5². Therefore, option D is the correct answer.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure, area of a largest square is 169 square units, area of a larger square is 144 square units and the area of a smaller square is 25 square units.

We know that, the area of a square is side².

Now, the side(a) of a largest square is side²=169

So, a=13 units

The side(b) of a larger square is side²=144

So, b=12 units

The side(c) of a smaller square is side²=25

Then, c=5 units

Here, a, b and c form a right angle triangle.

By using Pythagoras theorem, we get

a²=b²+c²

13²=12²+5²

Therefore, option D is the correct answer.

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According to the information and the graph, the best place for Lois Lane to stand to receive the keys from Superman is in the middle of the Krytonite cage because it is the closest place to the point where superman is standing.

The point where Lois Lane should stand is in the middle of the cage because there he will have a better chance of receiving the Kronite keys that he has. Additionally, this point is the closest to the point where Superman is standing so he wouldn't have to go near the krionite and could throw the keys from there.

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Answer:

8 and 1/3

Step-by-step explanation:

First, let's understand the situation. There is a 25 oz juice that is to be split 3 ways. To determine the amount of jucie each person gets, we will take the total amount of juice and divide it by the number of kids, 3. When we do this, we get 25/3. Since this fraction can;t be simplified into a whole number, we will need to turn 25/3 into a mixed number. To do this, we need to know how many times 3 goes into 25. 3 goes into 25 8 times with a remainder of 1. This remainder is put over 3, giving us the final answer, 8 and 1/3.

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Answer:

D

Step-by-step explanation:

The correct answer is D. −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.

The slope of a line represents the rate of change of one variable with respect to the other variable. In this case, the length of the icicle (y) is changing with respect to time (x). The slope of the line represents the change in the length of the icicle (y) for every additional hour (x).

Since the icicle is melting at a rate of 0.6 inches per hour, the length of the icicle decreases by 0.6 inches for every additional hour. The slope of the line representing this relationship is -0.6. This means that for every additional hour, the length of the icicle decreases by 0.6 inches.

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Answer:

17

Step-by-step explanation:

First you have to subtract 125-50 since we are trying to find the amount he made from selling t-shirts. That equals 85. So now we divide 85 by 5 and that gives us 85.

Answer:

Step-by-step explanation:

a._x+_=_

5x+40=125

    -40  -40

5x=85

/5

x=17

he sold 17 shirts

A vector w that is orthogonal to both u and v is w = (-1,-1,-1) and a vector x which is orthogonal to u and lies in the same plane defined by u and v is x = (-1,2,1).

The vectors are

u = (1, 0, 1)

v = (0, 2, 2)

If the scalar product of two vectors is equal to zero, then the vectors are orthogonal.

If we let let w = (a, b, c)

Then (u, w) ≥ 0

1×a + 0×b + 1×c = 0

a + c = 0

Subtract c on both side, we get

a = -c

and (v, w) = 0

0×a + 2×b + 2×c = 0

2b + 2c = 0

2(b + c) = 0

b + c = 0

b = -c

Then w = (-c, -c, -c)

If c=1

Then the orthogonal vector

w = (-1,-1,-1)

Let x = (x, y, z)

x is now orthogonal to u.

That is (u, x) = 0

1×x + 0×y + 1×z = 0

x + z = 0

x = -z

u × v = [tex]\begin{vmatrix}\hat{i} & \hat{j} & \hat{k}\\ 1 & 0 & 1\\ 0 & 2& 2\end{vmatrix}[/tex]

u × v = [tex]\hat{i}\begin{vmatrix} 0 & 1\\ 2& 2\end{vmatrix}-\hat{j}\begin{vmatrix} 1 & 1\\ 0& 2\end{vmatrix}+\hat{k}\begin{vmatrix} 1 & 0\\ 0& 2\end{vmatrix}[/tex]

u × v = [tex]\hat{i}[/tex](-2) - [tex]\hat{j}[/tex](2) + [tex]\hat{k}[/tex](2)

u × v = -2i-2j+2k

The given condition x lies on the plane u and v

(-2, -2, -2), x ≥ 0

-2x - 2y + 2z = 0

[x = -z]

2z - 2y + 2z = 0

-2y = -4z

y = 2z

That is x = (-z, 2z, z)

Now put z = 1

x = (-1,2,1)

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Answer:

i believe it is the last option.

Step-by-step explanation:

square units are units of area, so you'll want to find the SIDES and use those.
144 squared units would be 12 units per side.
25 would be 5, 169 would be 13.

pythagorean theorem is a^2 + b^2 = c^2, generally c is shown as the hypotenuse.

12^2 + 5^2 = 13^2 would be the last option given.

Answer:

120

Step-by-step explanation:

720/6 =120

The  probability that x is within 1 standard deviation from its mean value is 0.68.

Probability is the measure of the likelihood of an event occurring. In statistics, it is used to describe the chance of a particular value falling within a certain range.

A standard deviation is a measure of the spread of a set of data from its mean.

Typically, 68% of the data falls within 1 standard deviation from the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

In order to find the probability that x is within 1 standard deviation from its mean value, we need to use a normal distribution.

In a normal distribution, 68% of the data falls within 1 standard deviation from the mean.

So, in this case, the probability that x is within 1 standard deviation from its mean value is 0.68 or 68%.

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Answer:

  y = 0.4·5^x

Step-by-step explanation:

You want an exponential function y = a·b^x that passes through the points (1, 2) and (3, 50).

The given point values give two equations in two unknowns when used in the given exponential form:

  y = a·b^x

  2 = a·b^1

  50 = a·b^3

Dividing the second equation by the first, we find b:

  50/2 = (ab^3)/(ab)

  25 = b^2 . . . . . simplify

  5 = b . . . . . . . . . square root

Then the value of 'a' can be found from the first equation:

  2 = a·5

  a = 2/5 = 0.4

Using these values of 'a' and 'b', we have the exponential function ...

  y = 0.4·5^x

__

Additional comment

The exponential regression function of your calculator can tell you the same thing.

In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given, Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,

Since,

In 2 mins Mark's model train can go = 1/3 laps

Thus,

In 1 min Mark's model train can go = 1/3/2 laps

In 1 min Mark's model train can go = 1/6 laps

In 9 mins Mark's model train can go = 9/6 laps

In 9 mins Mark's model train can go = 1.5 laps

Therefore,  In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.

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f(-5) = 42

f(0) = 7

f(1) = 6

A function is a relationship that has a set of inputs and outputs. An example of a function is f(x) = x. The "(x)" in the parenthesis represents the input while the x on the left side represents the output. To compute the values of an output you plug in the input and replace all the variables with the input. E.g. to find f(1) we would replace all "x"s with 1 giving us f(1) = 1

Given f(x) = x² - 2x + 7 we want to find f(-5) , f(0) and f(1)

We can find these values by simply plugging in the values of the inputs and replacing all x's for them.

If f(x)= x² - 2x + 7

Then,

f(-5) = (-5)² - 2(-5) + 7                                                             simplify exponents

f(-5) = 25 - 2(-5) + 7                                                                  multiply -2 and -5

f(-5) = 25 + 10 + 7                                                                           add all values

f(-5) = 42

f(0) = (0)² - 2(0) + 7                                                                 simplify exponents

f(0) = 0 - 2(0) + 7                                                                       multiply 0 and -2

f(0) = 0 - 0 + 7                                                                                 add all values

f(0) = 7

f(1) = (1)² - 2(1) + 7                                                                     simplify exponent

f(1) = 1 - 2(1) + 7                                                                           multiply -2 and 1

f(1) = 1 - 2 + 7                                                           add and subtract the values

f(1) = 6

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Therefore , the solution of the given problem of triangle comes out to be x value of right triangle is 65° .

Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.

Here,

Given :

triangle has an right angle so its 90 degree.

The triangle sum of angle is 180 degree.

Thus,

=> x + 25° + 90° = 180°

=> x + 115° = 180°

=> x = 180° -115°

=> x = 65°

Thus , x value is 65° .

Therefore , the solution of the given problem of triangle comes out to be

x value of right triangle is 65° .

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Answer: The transformation is a reflection over the line x=0. The original square OABC is reflected over the line x=0 and the only invariant point is (0,2).

Step-by-step explanation:

This transformation is a reflection over the line with equation y = 2. The original square OABC is reflected over this line, mapping point A to C and C to A, while the only invariant point is (0, 2).

The average rate of change of V with respect to r over the interval [85,110] is 0.76 meters cubed per year per centimetre of rainfall.

V(r) = 0.2r² − 20r + 600

The average rate of change of V with respect to r over the interval [85,110] can be calculated by finding the derivative of V(r) and evaluating it at the midpoint of the interval, then dividing the result by the length of the interval. The derivative of V(r) is:

dV/dr = 0.4r - 20

The midpoint of the interval [85,110] is (85 + 110)/2 = 97.5. Evaluating the derivative at the midpoint, we get the following:

dV/dr = 0.4 × 97.5 - 20 = 19.0

The length of the interval is 110 - 85 = 25, so the average rate of change is:

The average rate of change = (dV/dr)/(110 - 85) = 19.0/25 = 0.76

So, the average rate of change of V with respect to r over the interval [85,110] is 0.76 meters cubed per year per centimetre of rainfall.

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--The given question is incomplete; the complete question is

"Eucalyptus trees, common in California and the Pacific Northwest, grow better with more water. Scientists in North Africa, analyzing where to plant trees, found that the volume of wood that grows on a square kilometre, in meters cubed, is approximated by V(r)=0.2r²−20r+600 where r is rainfall in centimetres per year, and 60≤ r ≤120. Calculate the average rate of change of V with respect to r over the interval [85,110]."--

The translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the points be represented as P and Q

Now , the coordinates of point P = P ( 0 , 0 )

And , the coordinates of the point Q = Q ( 5 , 4 )

when the points are translated up 3 units and left 2 units

The coordinates of the translated point will be ( x , y ) to ( x - 2 , y + 3 )

Substituting the values in the equation , we get

The coordinates of the translated point P' = P' ( -2 , 3 )

The coordinates of the translated point Q' = Q' ( 3 , 7 )

Hence , the translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )

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At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

Fahrenheit is named for German scientist Daniel Gabriel Fahrenheit, who was born there in 1686 as part of the Polish-Lithuanian Commonwealth. He was the first to develop a constant, accurate method of measuring temperature. At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

To assist us remember that we go from colder to hotter as we walk up the scale on our thermometer, let's label it. In other terms, a higher number of degrees Fahrenheit is hotter than a lower number.

[tex]$$\begin{aligned}& \text { Given:- } \mathrm{C}=\frac{5}{9}(\mathrm{~F}-32) \\& \Rightarrow \mathrm{F}=\frac{9}{5} \mathrm{C}+32\end{aligned}$$[/tex]

(I) If [tex]$F^{\prime}=F+1$[/tex]

[tex]$$\begin{aligned}\mathrm{C}^{\prime} & =\frac{5}{9}\left(\mathrm{~F}^{\prime}-32\right) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}+1-32) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}-32)+\frac{5}{9} \times 1 \\\mathrm{C}^{\prime} & =\mathrm{C}+\frac{5}{9}\end{aligned}$$[/tex]

Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Celsius.

Therefore, statement I exists true.

(II) If [tex]$\mathrm{C}^{\prime}=\mathrm{C}+1$[/tex]

[tex]$$\begin{aligned}& \mathrm{F}^{\prime}=\frac{9}{5} \mathrm{C}^{\prime}+32 \\& \mathrm{~F}^{\prime}=\frac{9}{5}(\mathrm{C}+1)+32 \\& \mathrm{~F}^{\prime}=\left(\frac{9}{5} \mathrm{C}+32\right)+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+1.8\end{aligned}$$[/tex]

Therefore, a temperature increase of 1 degree Celsius exists equivalent to a temperature increase of 1.8 degrees Fahrenheit.

Therefore, statement II exists true.

[tex]$$\begin{aligned}& \text { (III) If } F^{\prime}=F+\frac{5}{9} \\& C^{\prime}=\frac{5}{9}\left(F^{\prime}-32\right) \\& C^{\prime}=\frac{5}{9}\left(F+\frac{5}{9}-32\right) \\& C^{\prime}=\frac{5}{9}(F-32)+\frac{5}{9} \times \frac{5}{9} \\& C^{\prime}=C+\frac{25}{81}\end{aligned}$$[/tex]

Therefore, a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Fahrenheit exists equivalent to a temperature increase of [tex]$\frac{25}{81}$[/tex] degree Celsius.

Therefore, statement III exists false.

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The fraction of water is 7/12, when the ratio orange:pineapple:water=3:2 :7

A fraction represented with its quotient and remainder is a mixed fraction, and also one having a fraction and a whole number.

For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given that the ratio of orange: pineapple: water = 3: 2: 7.

consider orange=3x

pineapple=2x

water=7x

Total mix fraction=12x

To know the fraction value of water just divide the water by and total fraction.

fraction of water=7x/12x

fraction of water=7/12

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There is a 68% chance that a repair claim will be between $40 and $1020.

The normal distribution is a continuous probability distribution that is symmetric around the mean, with mean and variance being the same. In this case, the mean is $530 and the standard deviation is $490. This means that the repair claims are normally distributed, with the majority of the claims being between $530-$490 and $530+$490. This gives us a range of $40-$1020.

The normal distribution is often used to describe random variables because it is the most common probability distribution. In this case, it implies that the repair claims are randomly distributed around the mean of $530. The standard deviation of $490 indicates that there is a 68% chance that a repair claim will be within one standard deviation of the mean. In this case, that means that there is a 68% chance that a repair claim will be between $40 and $1020.

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The cost of 2 pounds of cherries without the coupon would be $6.50 x 2 = $13.

With the coupon, Madeline would have to pay $13 - $1 = $12 for 2 pounds of cherries.

The expression for the cost of buying x pounds of cherries with the coupon is:

(6.5*x) - 1

Seismic hazard analysis is a method of probability assessment that would most likely be used to assess the probability that a major earthquake will occur in California in the next three years.

Seismic hazard analysis is a method used to assess the probability of earthquakes occurring in a specific location, and it involves analyzing the historical records of earthquakes, geological data, and the tectonic plate movements in the area. This method is used to predict the likelihood of future earthquakes and their potential magnitude and intensity.

In the case of California, a seismic hazard analysis would likely be used to assess the probability of a major earthquake occurring in the next three years. The data collected from this analysis would help the government and the public prepare for potential earthquakes and minimize the damage caused by such events.

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If the instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour and electricity costs $0.30 per kilowatt hour, then the cost to run the player for an hour is $0.06 .

The cost of running a CD player for an hour can be calculated by multiplying (the amount of electricity it uses) by (the cost per kilowatt hour) .

According to the instruction booklet, the player uses 0.2 kilowatt of electricity per hour.

So, if electricity costs $0.30 per kilowatt hour, then

it would cost ⇒ 0.2 × $0.30 = $0.06 .

Therefore , it will take $0.06 to run the player for an hour.

The instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour. If electricity costs $0.30 per kilowatt hour, how much does it cost to run the player for an hour ?

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The domain for which functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal:{-2, 1/2}

When the functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal,

f(x) = g(x)

2x² - 1 = 1 - 3x

2x² + 3x -1 - 1 = 0

2x² + 3x - 2 = 0

We solve above quadratic equation to find the value of x.

2x² + 3x - 2 = 0

2x² + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(x + 2)(2x - 1) = 0

x + 2 = 0    OR    2x - 1 =  0

x = -2         OR     x = 1/2

This means, for x = -2 as well as x = 1/2 the functions f(x)=2x^2−1 and g(x)=1−3x are equal.

Thus, the required domain is: {-2, 1/2}

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(a) The answer is The Allen family earns $24,000 more than the Reed family.

(b) The answer is The Allen family earns more than about 87% of families in their county.

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Answer:

Step-by-step explanation:

The definite integral of the function (2x - 3) with respect to x can be found using the antiderivative, also known as indefinite integration.

The antiderivative of (2x - 3) is:

x^2 - 3x + C, where C is the constant of integration.

For the definite integral, we need to find the antiderivative over a given interval. To calculate the definite integral, we need to evaluate the antiderivative at the limits of the interval and subtract the values.

So, for example, if the interval is from a to b, the definite integral is given by:

∫_a^b (2x - 3) dx = (x^2 - 3x) |_a^b = (x^2 - 3x) evaluated at b - (x^2 - 3x) evaluated at a.

The definite integral of the function y³ (2y² – 3) with respect to y can be found in a similar way. The antiderivative of y³ (2y² – 3) can be found using power rule of integration.

The antiderivative of y³ (2y² – 3) is:

(1/4) y⁴ - 3y² + C, where C is the constant of integration.

The definite integral of the function can then be found by evaluating the antiderivative at the limits of the interval and subtracting the values, as described above.

Answers in image.

Step-by-step explanation:

To solve the questions,  use the power rule to solve.

Answer:

Step-by-step explanation:

The proportion of Year 13 pupils in the football club is 12/35. To convert this to a percentage, we need to multiply it by 100.

12/35 * 100 = 34.285714285714285 (approximately 34.3% when rounded to 1 decimal place)

Answer:

[tex] \frac{13}{35} \times \frac{100}{100} = 37.14\%[/tex]

Answer:

1. $16-20%= 12.8 US$

2. $x-20%=x

3. >>>>>?

Step-by-step explanation:

A 20% discount means that you subtract 20% of the normal price.  Suppose the normal price is $100.  20% of this is $20.  Subtract this from $100 and you have the new price---$80.

Note that "subtracting 20%" is the same as multiplying by 0.8----the general formula is:

discount price = normal price * (1-d)   , where d is the decimal equivalent of the percentage discount.

From the example above:

discount price = normal price * (1-d) = 100(0.8)

to go the other way, simply rearrange the formula:

normal price = discount price / (1-d)

If the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.

The graph is a function if any vertical line drawn through it can cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through the graph at two or more different places.

A mathematical function from a set X to a set Y assigns exactly one element of Y to each element of X. The function's domain and codomain, respectively, are the sets X and Y as a whole. Initially, functions represented the desired relationship between two fluctuating values.

A function is a relation that specifically links members of one set to those of another set. Formally speaking, a function from to is an object such that each is specifically connected with an object. Therefore, a function is a many-to-one (or occasionally, a one-to-one) relation.

Let the given function be f(x) = x⁵ + (x + 3)²

When x = -1 then f(-1) = (-1)⁵ + (-1+3)² = -1 + 4 = 3.

Therefore, the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.

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