10
Which of the following is the midpoint between (3, 2) and (-3, 4)?


(0, 3)


(0, 3/2)


(6, 3/2)


(-6, 3)

Answer:

16 dollars

Step-by-step explanation:

114÷6=19-3 is 16

Answer:

8

Step-by-step explanation:

1 quart=4 cups so 4x2=8

Answer:

105

Step-by-step explanation:

Divide 951 by 9

The expected number of people out of 700 to order plain vanilla ice cream flavor is given as follows:

b. 224 people.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of 3 x 50 = 150 people surveyed, 17 + 15 + 16 = 48 ordered plain vanilla ice cream, hence the probability of a person ordering plain vanilla ice cream flavor is given as follows:

p = 48/150

Then, out of 700 people, the expected number of people to order the plain vanilla flavor is given as follows:

700 x 48/150 = 224 people.

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Answer: $54 / 3 = $27 for each girl

Step-by-step explanation:

Answer:

33 : 15 : 6

Step-by-step explanation:

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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The reasonable amount Ester will spend on vegetables is $27

The amount is the value in $ which Ester will spend on vegetable and fruits in the grocery market. To determine the amount we have to determine the average of the current  expenditure for the current period

The given parameters are

The range of values to spend

$40 to $50

Percentage of amount to spend = 20%

Number of weeks = 3

Average amount to be spend = (40+50)/2 = 90/2 = $45

(20/100)*45/1 = 9

In the next 3 weeks

In the nest 3 weeks Ester spends ($3*9)= $27

In conclusion, Ester spends $27 in the next three weeks

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Answer:

I want the class stage or level,

before I slove this question

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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Answer:

2/12 or 1/6

Step-by-step explanation:

Make common denominators, 3/4 turns into 9/12. Take away 9/12 from 11/12, simplify if needed, and boom! done!

Answer: -3 \(\frac{1}{4}\)

Step-by-step explanation:

   Given:

       -16 5/8 - (-13 3/8)

   Minus times a minus is positive:

       -16 5/8 + (13 3/8)

   Calculate -16 + 13 and -5/8 + 3/8:

       -3 2/8

   Simplify the fraction:

       -3 1/4

The estimation for Diego based on the information about the weight is 18 grams.

Estimation is the process of determining an estimate or approximation, which is a value that can be used for a specific purpose despite the fact that the input data may be incomplete, uncertain, or unstable. When we use approximate values in a calculation to give an approximate, predicted answer rather than an exact answer, we are using estimation. By using round numbers, estimating calculations make them more manageable.

From the information, the four rocks have the following weights: 4.29 grams, 4.71 grams, 3.55 grams, 5.48 grams.

The estimation will be:

4.29 grams = 4 grams

4.71 grams = 5 grams

3.55 grams = 4 grams

5.48 grams = 5 grams

The approximate weight will be:

= 4 + 5 + 4 + 5

= 18 grams.

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Given the frequency and number of possible outcomes, the number of days that must pass before it becomes probable that Janice will have had to pick up lunch at least once is 8.

Note that the probability of any of the staff at the office picking the food is 1/8.

Even if She does not pick up lunch on her first day or second, the number of days that must pass to make sure that Janice picks up lunch AT LEAST once is 1 in 8 days.

The formula to compute the probability of an event is equivalent to the ratio of favorable outputs to the total number of outputs. It is to be noted that probabilities always range between 0 and 1.

The expression is given as:

P (E) = f/O; where

P(E) is the Probability of an event E happening;

f =  The number of possible outcomes for an event (frequency)

n = Total number of outputs that are likely

Hence,

P(E) = 1/8

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Answer:

B. -15

Step-by-step explanation:

Took the test, this question was correct when you choose -15.

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

(This is technically a personal opinion question) In MY opinion all government run things from libraries to schools to the military come from taxes. If you don't agree with how the government spends the money that you pay in taxes yet enjoy/use government facilities then you have no room to complain and not pay your taxes.

The value of 14.5% of 1,800 is 261 by using the concept of percentage.

In mathematics, a percentage is a value or ratio expressed as a fraction of 100.

The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.

A % is a relative figure that indicates one-tenth of a quantity. One percent (symbolized 1%) is the one-hundredth part; consequently, 100 percent denotes the complete amount, and 200 percent specifies twice the supplied amount.

Given,

14.5% of 1,800

=(14.5/100)×1800

=261

Therefore, the answer is 261.

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Hi there!

\(\huge\boxed{=27}\)

\(\frac{3^{2}*(2^{3}+4)}{2^2}\)

Use the order of operations to solve. Begin by evaluating the inside of the parenthesis.

Evalute 2³ = 8:

\(\frac{3^{2}*(8+4)}{2^2}\)

Simplify:

\(\frac{3^{2}*(12)}{2^2}\)

Evaluate each power. 3² = (3 × 3) = 9, and 2² = (2 × 2) = 4:

\(\frac{9*(12)}{4}\)

Simplify:

\(\frac{108}{4} = 27\)

Answer:

\(\text{Midpoint of $AC$}=\left(-2,2\right)\)

\(\text{Midpoint of $AB$}=\left(\dfrac{5}{2},3\right)\)

\(\text{Slope of midsegment}=\dfrac{2}{9}\)

\(\text{Slope of $AC$}=3\)

\(\text{Slope of $BC$}=\dfrac{2}{9}\)

\(\text{Length of midsegment}=\dfrac{\sqrt{85}}2\)

\(\text{Length of $BC$}=\sqrt{85}\)

Step-by-step explanation:

Given points:

To determine the midpoints of AC and AB, substitute the given points into the midpoint formula.

\(\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}\)

\(\begin{aligned}\text{Midpoint of $AC$}&=\left(\dfrac{x_C+x_A}{2},\dfrac{y_C+y_A}{2}\right)\\\\&=\left(\dfrac{-3-1}{2},\dfrac{-1+5}{2}\right)\\\\&=\left(\dfrac{-4}{2},\dfrac{4}{2}\right)\\\\&=\left(-2,2\right)\end{aligned}\)

\(\begin{aligned}\text{Midpoint of $AB$}&=\left(\dfrac{x_B+x_A}{2},\dfrac{y_B+y_A}{2}\right)\\\\&=\left(\dfrac{6-1}{2},\dfrac{1+5}{2}\right)\\\\&=\left(\dfrac{5}{2},\dfrac{6}{2}\right)\\\\&=\left(\dfrac{5}{2},3\right)\end{aligned}\)

\(\hrulefill\)

\(\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}\)

To determine the slope of the midsegment, substitute the midpoints of AC and AB into the slope formula:

\(\begin{aligned}\text{Slope of midsegment}&=\dfrac{y_{AB}-y_{AC}}{x_{AB}-x_{AC}}\\\\&=\dfrac{2-3}{-2-\frac{5}{2}}\\\\&=\dfrac{-1}{-\frac{9}{2}}\\\\&=\dfrac{2}{9}\end{aligned}\)

Therefore, the slope of the midsegment is 2/9.

To find the slope of AC, substitute the points A and C into the slope formula:

\(\begin{aligned}\text{Slope of $AC$}&=\dfrac{y_{C}-y_{A}}{x_{C}-x_{A}}\\\\&=\dfrac{-1-5}{-3-(-1)}\\\\&=\dfrac{-6}{-2}\\\\&=3\end{aligned}\)

Therefore, the slope of the AC is 3.

**Note** There may be an error in the question. I think you are supposed to find the slope of BC (not AC) since there is no relationship between the slopes of the midsegment and AC, but there is a relationship between the slopes of the midsegment and BC.  

\(\begin{aligned}\text{Slope of $BC$}&=\dfrac{y_{C}-y_{B}}{x_{C}-x_{B}}\\\\&=\dfrac{-1-1}{-3-6}\\\\&=\dfrac{-2}{-9}\\\\&=\dfrac{2}{9}\end{aligned}\)

The slope of BC is 2/9, so the slopes of the midsegment and BC are the same. This implies that the midsegment and BC are parallel.

\(\hrulefill\)

\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)

To find the length of the midsegment, substitute the endpoints (-2, 2) and (5/2, 3) into the distance formula:

\(\begin{aligned}\text{Length of midsegment}&=\sqrt{\left(\frac{5}{2}-(-2)\right)^2+(3-2)^2}\\\\&=\sqrt{\left(\frac{9}{2}\right)^2+(1)^2}\\\\&=\sqrt{\frac{81}{4}+1}\\\\&=\sqrt{\frac{85}{4}}\\\\&=\dfrac{\sqrt{85}}2\end{aligned}\)

To find the length of the BC, substitute points B and C into the distance formula:

\(\begin{aligned}\text{Length of $BC$}&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-3-6)^2+(-1-1)^2}\\&=\sqrt{(-9)^2+(-2)^2}\\&=\sqrt{81+4}\\&=\sqrt{85}\end{aligned}\)

Therefore, the length of BC is twice the length of the midsegment.

Answer:

D

Step-by-step explanation:

angle ABC=angle ADC

angle BAC=angle DCA

AC=CA

Answer:

12 yrs old

Step-by-step explanation:

consevutive integers that add up to 39

12+13+14=39

the youngest is 12

Answer:

12 years old

Step-by-step explanation:

quick maths

Answer:

20

Step-by-step explanation:

The theoretical probability of drawing 2 red marbles from the bag with replacement is one-fifth, which means that the probability of drawing 2 red marbles in any one trial is 1/5 or 0.2.

The number of times Jonah is expected to select 2 red marbles in 100 trials can be predicted using the expected value formula:

Expected value = (Number of trials) x (Probability of success in one trial)

Expected value = 100 x 0.2

Expected value = 20

Therefore, a reasonable prediction of the number of times Jonah will select 2 red marbles in 100 trials is 20. Therefore, the answer is 20.

Answer: 20 i took the test

Step-by-step explanation:

The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The number of color are possible  \(\left n} \atop }} \right. C _r = 1215450\)

Step-by-step explanation:

From the question we are told that  

   The number of  colors is  r = 4

    The sample size n =  75

The number of color that are possible can be mathematically evaluated as

       \(\left n} \atop }} \right. C _r = \frac{n !}{ (n-r)! r!}\)

substituting values

         \(\left n} \atop }} \right. C _r = \frac{75 !}{ (75-4)! 4!}\)

       \(\left n} \atop }} \right. C _r = \frac{75 !}{ (71)! 4 !}\)

       \(\left n} \atop }} \right. C _r = \frac{75 *74 * 73* 72 * 71!}{ (71)! (4*3*2 *1)}\)

        \(\left n} \atop }} \right. C _r = 1215450\)

The amount invested in the account with 8% interest is $410 and the  amount invested in the account with 7% interest is $260.

The first step is to form a system of equations using the information in the question:

x - y = 150 equation 1

0.08x + 0.07y = 51 equation  2

Where:

The elimination method would be used to determine the required values

Multiply equation 1 by 0.08

0.08x - 0.08y = 12 equation 3

Subtract equation 3 from equation 2:

0.15y = 39

y = 39 / 0.15

y = 260

Substitute for y in equation 1 :

x - 260 = 150

x = 260 + 150

x = 410

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Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

-9/2

Step-by-step explanation:

Hope this helped!

y=\(\frac {-9}{2}\)

Answer:

solution given :

\(-\frac {1}{y+5}=-2 \)

here - and - will be cancelled and former

\(\frac {1}{y+5}=2 \)

now doing criss cross multiplication

we get

1=2 (y+5)

opening bracket

1=2y+10

1-10=2 y

y=\(\frac {-9}{2}\)

Answer:

Area is  220 cm²

Step-by-step explanation:

Firstly divide the polygon into  rectangle and triangle

For rectangle  area

 Area = A  =  L × W = 11 × 18 = 198 cm²

For triangle

Area =  A =  1/2 bh = 1/2 × (15-11) × (18-7) = 1/2 × 4 ×11 = 44/2 = 22 cm²

Add them

     198 + 22 = 220cm²

Mark brainliest if you understand