The scatter plot shows the number of chin-ups and push-ups several students did.

Answer:

a. The x-coordinate of the minimum point of this parabola is halfway between the two roots (-1 and 2). So the x-coordinate here is 1/2, and we have:

[tex]f( \frac{1}{2} ) = { (\frac{1}{2} )}^{2} - \frac{1}{2} - 2 = - 2 \frac{1}{4} [/tex]

So the coordinate of the turning point is (1/2, -2 1/4), or (.5, -2.25).

b. The roots of this parabola are at (-1, 0) and (2, 0).

Norma's expenses and earnings will both be $89, and she needs to teach 8 classes during her first month to earn back her certification cost.

To calculate Norma's expenses and earnings, we need to first determine how many classes she needs to teach to earn back her certification cost.
Let x be the number of classes Norma teaches in her first month.

Her earnings for the first month will be her base salary plus the additional amount per class, which can be represented as 57 + 4x.
To find out how many classes Norma needs to teach to cover her certification cost, we can set up the equation:
57 + 4x = 89
Now, we need to solve for x:

4x = 89 - 57
4x = 32
x = 8
So, Norma needs to teach 8 classes to earn back her certification cost.

Now, we can calculate Norma's total expenses and earnings for the first month.

Her expenses are the certification cost, which is $89.

Her earnings are the base salary plus the additional amount per class:
Earnings = 57 + 4 * 8
Earnings = 57 + 32
Earnings = $89.

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The answer of the given question based on quadratic equation is the value of c is -43.

An equation is mathematical statement that shows the two expressions are equal. It consists of two parts, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can be made up of numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

For example, the equation 2x + 3 = 7 shows that the expression 2x + 3 is equal to 7. The variable x represents an unknown quantity that can be solved for by manipulating the equation using algebraic techniques.

If the product of the roots of the quadratic equation y = 4x² + 16x + c is -43/4, we can use the fact that the product of the roots is equal to c/4 to solve for c.

So, we have:

[tex]\frac{c}{4} =-\frac{43}{4}[/tex]

Multiplying both sides by 4, we get:

c = -43

Therefore, the value of c is -43.

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From the given quadratic equation the value of c=-43.

What is quadratic equation?

Quadratic equations are second-degree algebraic expressions that is it an equation of degree 2 and are of the form ax² + bx + c = 0.

where a≠0.

Given quadratic equation is

 y= 4x² +16x+c

Comparing with the quadratic equation y= ax²+bx+c₁ we get,

a= 4, b= 16, c₁= c

Product of the roots is c₁/a

So for this problem product of the roots will be c/4

Here given the product of the roots of the given quadratic equation is -43/4

Equating both we get,

c/4= -43/4

c=-43

Hence, the value of c= -43.

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Depending on the given angle measures of the triangle, the angle measures of triangle ABC are either 30°, 60°, and 90° or 90°, 60°, and 30° or 60°, 90°, and 30°.

Triangle ABC with angle measures ∠A, ∠B, and ∠C given as:

Therefore, depending on the given angle measures of the triangle, the angle measures of triangle ABC are either 30°, 60°, and 90° or 90°, 60°, and 30° or 60°, 90°, and 30°.

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What are the angle measures of triangle abc?

a)∠a = 30 , ∠b = 60, ∠c= 90

b)∠a=90, ∠b= 60, ∠c= 30

c)∠a= 60, ∠b= 90, ∠c=30

d)∠a = 90, ∠b = 30, ∠c = 60

For the given similar figures, the area of larger parallelogram is calculated to be 1470 ft².

In Euclidean geometry, a parallelogram is known to be a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. Opposite or opposite sides of a parallelogram have equal length, and opposite angles of a parallelogram are equal.

Parallelograms can be divided into different types according to different properties. They are mainly divided into three special types.

Given,

For the smaller parallelogram:

Area  = 30 ft²

Base = 5 ft

Height = ?

Area = Base × Height

30 = 5 × Height

Height = 30/5

Height = 6 ft

Since the parallelograms are similar, so the proportion of their base and height will be similar as well:

Given, that the base of larger parallelogram is 35 ft,

Base/Height = 5/6 = 35/Height

Height = (35 × 6)/5

Height = 42 ft

Now the area of larger parallelogram will be:

Area = Base × Height

Area = 35 × 42

Area = 1470 ft²

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Answer:

x = 23

Step-by-step explanation:

180 - 100 = 80

51 + 80 = 131

180- 131=49

49= 2x +3

49 - 3= 46

46=2x

46/ 2= 23

X= 23

Answer:

Step-by-step explanation:

is there a height? Is the triangle with a 90 degrees angle? Is there any other conditions that are given?

Step-by-step explanation:

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

Answer:

3.13

Step-by-step explanation:

The price of all three ropes together - $9.38

Price of one unit -9.38/3.=

3.12666 ; Nearest round figured cent would be $3.13

The derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

From the question, we have the following parameters that can be used in our computation:

y = 6x^3

To find the derivative of y with respect to x, we can use the power rule of differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).

Using this rule, we can differentiate y = 6x^3 as follows:

dy/dx = d/dx (6x^3)

= 6 * d/dx (x^3)

= 6 * 3x^2 (applying the power rule with n=2)

= 18x^2

Therefore, the derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

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X, the number of correct guesses out of all the attempts for members in the group, follows a binomial distribution

The theoretical probability of one correct guess is the total number of correct guesses divided by the total number of guesses, which in this case is 11/15 or 0.73.

X represents the number of correct guesses out of all the attempts for members in the group. Since each member's guess is independent of the others, and each guess has the same probability of being correct, X follows a binomial distribution.

The binomial distribution is characterized by two parameters: the number of trials (n) and the probability of success on each trial (p). In this case, n is the total number of guesses, which is 15, and p is the theoretical probability of one correct guess, which is 0.73.

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The given question is incomplete, the complete question is:

Theoretical Probability of one correct guess # of Correct Total # of Group Member Guesses Guesses Jay 3 Amanda 4 Nicholas 4 Overall 11 5 5 15 2.) Let X represent the number of correct guesses out of all the attempts for members in your group. What kind of distribution does X have? Justify your response, indicating values for any of the variables that describe the distribution.

There is a  there is a 3.125% chance that all five customers will give Steve a tip.

To calculate the probability of all five customers giving Steve a tip, we need to multiply the probability of one customer giving a tip (0.5) by itself five times since each customer's tip is an independent event. So, the probability is:

0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125

So, there is a 3.125% chance that all five customers will give Steve a tip.

To simulate this situation, we could use a random number generator that generates either 0 or 1, with a 50% chance of each. We could then repeat this process five times and count the number of times we get five ones (representing all five customers giving a tip). We could then use the proportion of times we get five ones out of the total number of simulations to estimate the probability of all five customers giving a tip. We would want to repeat the simulation many times to get a more accurate estimate.

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Answer:

  radius : height = 7 : 3

Step-by-step explanation:

You want the ratio of the base radius to the height of a cylinder that has 30% of its surface area as lateral area.

The lateral area of a cylinder is ...

   LA = 2πrh

The base area of a cylinder is ...

  A = 2(πr²) = 2πr·r

Then the ratio of lateral area to total area is ...

  [tex]\dfrac{\text{LA}}{\text{LA+A}}=\dfrac{2\pi rh}{2\pi rh+2\pi rr}=\dfrac{h}{h+r}=\dfrac{30}{100}[/tex]

Inverting this relation lets us solve for r/h:

  [tex]\dfrac{h+r}{h}=\dfrac{100}{30}\\\\1+\dfrac{r}{h}=1+\dfrac{70}{30}\\\\\boxed{\dfrac{r}{h}=\dfrac{7}{3}}[/tex]

The approximate probability that Maurice will obtain a sample proportion less than 0.06 is 0.2119, rounded to three decimal places.

The population proportion is p = 0.08 since we are aware that the actual percentage of students who have not declared a major is 0.08. We are asked to estimate the likelihood that Maurice will acquire a sample fraction smaller than 0.06 from a simple random sampling of n = 250 students.

The sample proportion p' is a random variable with a mean equal to the population proportion p and standard deviation σ = √(p(1-p)/n). In this case, we have:

p = 0.08

n = 250

σ = √(0.08×(1-0.08)/250)

  = 0.025

To find the probability that p' < 0.06, we can standardize the variable using the standard normal distribution:

z = (p' - p) / σ

z = (0.06 - 0.08) / 0.025

 = -0.8

Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score less than -0.8 is approximately 0.2119.

Therefore, the approximate probability that Maurice will obtain a sample proportion less than 0.06 is 0.2119, rounded to three decimal places.

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The required diameter of the sphere for the given volume of the sphere is equal to 12.2 cm (rounded to one decimal place)

Volume of the sphere = 944cm^3

Let us consider V be the volume of the sphere.

And r be the radius of the sphere.

The formula for the volume of a sphere is,

V = (4/3) × π × r^3

Solve for the radius of the sphere by rearranging the formula as follows,

⇒ r^3 = (3/4) × (V/π)

⇒r = [(3/4)×(V/π)]^(1/3)

Substituting V = 944 cm^3, we have,

⇒ r = [(3/4) ⇒ (944/π)]^(1/3)

⇒r ≈ 6.08 cm

⇒r ≈ 6.1 cm (rounded to one decimal place)

The diameter of the sphere is twice the radius, so the diameter is,

d = 2r

   ≈ 12.2 cm (rounded to one decimal place)

Therefore, the diameter of the sphere with a volume of 944 cm^3 to the nearest tenth of a centimeter is 12.2 cm.

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Answer:

Part 1: x = -2

Part 2: x = 56

Step-by-step explanation:

Part 1:

12x + 9 = -15

Given that-

12x + 9 = -15

12x + 9 - 9 = -15 -9                >> Subtract 9 to both sides

12x = -24

12x/12 = -24/12                    >> Divide both sides by 12

x = -2

Check Answer:

12(-2) + 9 = -15                 >> 12 × -2 = -24

-24 + 9 = -15                   >> -24 + 9 = -15

-15 = -15                        >> Correct

Part 2:

x/7 - 4 = 4

Given that-

x/7 - 4 = 4

x/7 - 4 + 4 = 4 + 4                 >> Add 4 to both sides

x/7 = 8                

7x/7 = 8 × 7                             >> Multiply both sides by 7

x = 56

Check Answer-

Substitute x in the equation the check.

56/7 - 4 = 4              >> 56/7 = 8

8 - 4 = 4                  >> 8 - 4 = 4

4 = 4                        >> Correct

RevyBreeze

the correct expressions to represent the current value of Gabriella's stock accounts are 1.05d for stock A, 0.95d for stock B, d(1-0.05) for stock B, and d(1+0.05) for stock A.

How to estimate sell?

To calculate the value of Gabriella's stocks, we need to consider the changes in the stock prices of A and B over the year.

We know that stock A has increased by 5%, so its current value is 1.05 times its original value, which means the value of Gabriella's investment in stock A is now 1.05d.

On the other hand, stock B has decreased by 5%, which means its current value is 0.95 times its original value. Thus, the value of Gabriella's investment in stock B is now 0.95d.

Therefore, the expressions that could be used to represent the current value of Gabriella's stock accounts are 1.05d for stock A and 0.95d for stock B.

The expression d+0.05d is incorrect because it assumes that both stocks have increased by 5%, which is not the case. The expressions d-0.5d and d+0.5d are incorrect because they do not take into account the percentage changes in the stock prices. The expression d-0.05d is incorrect because it assumes that both stocks have decreased by 5%, which is not the case.

The expression 0.95d is correct but only represents the value of stock B, while the expression d(1-0.05) is correct for stock B, but d(1+0.05) is correct for stock A.

In summary, the correct expressions to represent the current value of Gabriella's stock accounts are 1.05d for stock A, 0.95d for stock B, d(1-0.05) for stock B, and d(1+0.05) for stock A.

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The value of x in the triangles in diagram A and B is 9.28 respectively.

Triangle is a plane shape that has three sides.

(A) To solve for x in the triangle in diagram A, we use the formula below

Formula:

Where:

Substitute these values into equation 1 and solve for x

(B) Similarly, to solve for x in the triangle in diagram B, we use the formula below

Formula:

Where:

Substitute these values into equation 2 and solve for x

Hence, the values of x in A and B is 9.28 respectively.

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Answer:

Step-by-step explanation:

So we know by Vertical Angles the opposite is contgruent and since j shares many angles one line its supplementry so we have

j + 76 + 90 = 180 suppl. angles there for j equals 14 degrees ( dont let the h fool you)

We need to find the probability that the two winners line in Pike.

We know that 2 out of the 10 customers who entered the drawing live in Pike.

Thus, the probability of the first winner line in Pike is:

[tex]\dfrac{2}{10}[/tex]

Then, considering the first winner live in Pike, there are left 9 customers, and 1 of them live in Pike. Thus, the probability that the second winner lives in Pike is:

[tex]\dfrac{1}{9}[/tex]

Now, the probability that the first one lives in Pike and the second one also lives in Pike is the product of the two probabilities we found:

[tex]\dfrac{2}{10}\times\dfrac{1}{9}=\dfrac{2}{10\times9} =\dfrac{1}{10\times4.5} =\dfrac{1}{45}[/tex]

Therefore, the probability that both winners live in Pike is:

[tex]\dfrac{1}{45}[/tex]

The test statistic for the given hypothesis test is 2.31, indicating a significant difference between the sample mean and the hypothesized mean. The p-value is less than 0.025, and at a significance level of 0.05, the null hypothesis is rejected, concluding that the true population mean is greater than 12. The rejection rule using the critical value is to reject the null hypothesis if the test statistic is greater than 1.645.

To compute the test statistic, we first need to calculate the standard er ror of the mean:

SE = /sqrt(n) = 4.32/sqrt(25) = 0.864

Then, we can calculate the test statistic:

z = (sample mean - hypothesized mean)/SE = (14 - 12)/0.864 = 2.315

Rounding to 2 decimals, the test statistic is 2.31.

The degrees of freedom for this test are 24 (n-1), so we can find the range for the p-value using a t-distribution table with 24 degrees of freedom. For a two-tailed test at a significance level of 0.05, the range is between 2.064 and 2.492. Since the test statistic (z = 2.31) falls outside this range, the p-value is less than 0.025.

At a significance level of 0.05, since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the true population mean is greater than 12.

The rejection rule using the critical value at a significance level of 0.05 is to reject the null hypothesis if the absolute value of the test statistic is greater than 1.96 (for a two-tailed test) or if the test statistic is greater than 1.645 (for a one-tailed test).

In this case, the test is one-tailed and the critical value is 1.645 (obtained from a t-distribution table with 24 degrees of freedom). Since the test statistic (z = 2.31) is greater than 1.645, we reject the null hypothesis.

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Answer:

5%

It is 5% because in the section, 3.0-3.5, it says 5, which also counts for 5% of the babies.

Absolute Value Equation for a Horizontal Line Passing Through Two Points -1/2 and 3/2.

The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:

| x - 1 | = 1/2

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The value of the logarithm of numbers is 1/4

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given logarithm is 1 + log₇25

Simplifying this we have log₇25 = -1

Taking the logarithm of both sides we have

log₇25  = -100x

25 =7⁻¹⁰⁰ˣ

100x = 25

Dividing by 100

x = 25/100

X = 1/4

Therefore the value of the logarithm is 1/4

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15(x+3) = 2x(12)

15x+45 = 24x

45 = 9x

x = 5

From the 12 listed amount, the amount which are within 1.5 standard deviation of the mean are (E) Eleven.

The term "Standard-deviation" is defined as a statistical measure of amount of variation of a set of data points from mean value.

The amounts which are within 1.5 standard deviation means can eb calculated by the formula :

⇒ {mean - 1.5×(S.D.), mean + 1.5×(S.D.)}

Substituting the values,

We get,

⇒ {8.1 - 1.5×0.3,  8.1 + 1.5×0.3}

⇒ {7.65 , 8.55}.

The 12 listed amount are : {8.22, 7.51, 7.86, 8.36, 7.83, 8.30, 8.09, 8.01, 7.73, 8.53, 8.25, 7.96},

We can see that, from the 12 listed amounts, only 7.51 is out of this rage and the remaining 11 amounts are within this rage.

Therefore, the correct option is (E) Eleven.

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The given question is incomplete, the complete question is

A vending machine is designed to dispense 8 ounces of coffee into a cup. after a test that recorded the number of ounces of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. if the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

7.51, 8.22, 7.86, 8.36, 8.09, 7.83, 8.30, 8.01, 7.73, 8.25, 7.96, 8.53.

(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

Answer:

ITS 15 ITS A C = 15

Step-by-step explanation:

HOPE THIS HELPS

PL Z GIVE BRAINLIEST

The length decreased by 6 cm (from 18 cm to 12 cm) and the width increased by 3 cm (from 9 cm to 12 cm) indeed form a square with an area of 135 cm², which is 27 cm² smaller than the area of the rectangle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Let's start by defining the variables we will use:

Let L be the original length of the rectangle.

Let W be the original width of the rectangle.

Let A be the area of the rectangle.

From the problem statement, we can set up the following equations:

(L - 6) = (W + 3) (the length decreased by 6 cm is equal to the width increased by 3 cm, forming a square)

(L - 6)(W + 3) - 27 = A (the area of the square is 27cm² smaller than the area of the rectangle)

Simplifying the first equation, we get:

L - W = 9

Solving for one variable in terms of the other, we can express L in terms of W:

L = W + 9

Substituting this expression into the second equation, we get:

(W + 3 - 6)(W + 3) - 27 = A

W(W + 6) - 27 = A

Expanding and simplifying, we get:

W² + 6W - 27 = A

Now, we can use the first equation to substitute for L in terms of W, and express A solely in terms of W:

A = LW

A = (W + 9)W

A = W² + 9W

Substituting this expression for A into the previous equation, we get:

W² + 6W - 27 = W² + 9W

Simplifying, we get:

3W = 27

W = 9

Substituting this value for W into the expression for L, we get:

L = W + 9 = 9 + 9 = 18

Therefore, the original length and width of the rectangle are 18 cm and 9 cm, respectively, and the area of the rectangle is:

A = LW = 18 x 9 = 162 cm²

We can check that the length decreased by 6 cm (from 18 cm to 12 cm) and the width increased by 3 cm (from 9 cm to 12 cm) indeed form a square with an area of 135 cm², which is 27 cm² smaller than the area of the rectangle.

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Answer:

252

Step-by-step explanation:

lol I take rsm too and I just guessed and checked

The answer of the given question based on the Probability is,  the experimental probability that the card selected was a K or 6 is 19/100 or 0.19.

What is  probability ?

Experimental probability is a method of determining the probability of an event occurring based on experimental data. It involves conducting an experiment or observation and recording the number of times the event of interest occurs, then calculating the ratio of the number of times the event occurred to the total number of trials or observations.

Experimental probability is often used in fields such as science, engineering, and social sciences, where empirical data is collected through experimentation or observation. It is a useful tool for making predictions and testing hypotheses based on real-world data.

The number of times a K or 6 was drawn is the sum of their respective frequencies, which is:

Frequency of K or 6 = Frequency of K + Frequency of 6 = 12 + 7 = 19

The total number of cards drawn is 100, so the experimental probability of drawing a K or 6 is:

Experimental probability = Frequency of K or 6 / Total number of cards drawn = 19 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 19/100 or 0.19, which is approximately equal to 4/21 or 0.1905 when expressed as a fraction or rounded to four decimal places.

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The experimental likelihood that the chosen card was either a K or a 6 is 13/100, or 0.13 or 13%.

The likelihood of results occurring is examined in the study of probability, which is based on the ratio of likely to improbable scenarios.

It is necessary to add the frequencies of cards K and 6 and divide by the total number of draws in order to determine the experimental probability of drawing a K or 6:

Frequency οf K οr 6 = 7 + 6 = 13

Tοtal number οf draws = 4 + 7 + 5 + 6 + 7 + 6 + 8 + 10 + 7 + 10 + 8 + 12 + 10 = 100

Experimental prοbability οf drawing a K οr 6 = Frequency οf K οr 6 / Tοtal number οf draws = 13 / 100

Therefore, the experimental likelihood that the chosen card was a K or 6 is 13/100, or 0.13 or 13%.

The correct response is 8 over 13, as that is the easiest answer to the 13/100 question.

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