June has $1.95 in dimes and nickels. She has a total of 28 coins. How many of each type of coin does she have?

Please show work!!

Answer:

1) P(258.5-cm < M < 259-cm) = 8.71%.

2) P17 = 125.57cm

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question 1:

Mean of 258.5-cm and a standard deviation of 2.3-cm, which means that \(\mu = 258.5, \sigma = 2.3\)

Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.

This is the pvalue of Z when X = 259 subtracted by the pvalue of Z when X = 258.5.

X = 259

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{259 - 258.5}{2.3}\)

\(Z = 0.22\)

\(Z = 0.22\) has a pvalue of 0.5871

X = 258.5

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{258.5 - 258.5}{2.3}\)

\(Z = 0\)

\(Z = 0\) has a pvalue of 0.5

0.5871 - 0.5 = 0.0871

0.0871*100% = 8.71%. So

P(258.5-cm < M < 259-cm) = 8.71%.

Question 2:

Mean of 127.1-cm and a standard deviation of 1.6-cm, which means that \(\mu = 127.1, \sigma = 1.6\)

Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.

This is the 17th percentile, which is X when Z has a pvalue of 0.17. So X when Z = -0.954.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.954 = \frac{X - 127.1}{1.6}\)

\(X - 127.1 = -0.954*1.6\)

\(X = 125.57\)

P17 = 125.57cm

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

45 square ft^2

Step-by-step explanation: The formula of the area of the trapezoid is A=(a+b)/2 x h. A represents the top while b represents the bottom. 15+3=18 and 18/2=9. If multiply the result by 5, you get 45 as the answer.

Answer:

~77°

Step-by-step explanation:

cosQ = 9/40

inverse cosine(9/40) ≈ 77° = Q

Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)

Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

Answer:

-40

Step-by-step explanation:

So what this question is basically saying is that you have to multiply -4 by -2 first to get 8 and then you multiply that by -5 hence getting the answer of -40

Using the length formula we know that the length of the given arc is 30.144 miles.

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter.

So, the formula to find the length of the arc is:

Length of an Arc = θ × r

Now, insert values and calculate as follows:

Length of an Arc = θ × r

Length of an Arc = 4π/5 × 12

Length of an Arc = 4π/5 × 12

Length of an Arc = 12.56/5 * 12

Length of an Arc = 2.512 * 12

Length of an Arc =  30.144

Therefore, using the length formula we know that the length of the given arc is 30.144 miles.

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The amount of the area of the home used and the total area of the second property are 26.25 acres and 20.625 acres respectively.

The amount of land to be used for a home is the difference between the total land area and the area to be used for land :

Land Area of second property = 0.78 times the land ares

Therefore, the total area of the second property is 20.625 acres.

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The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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Answer:

1 It changed their way of life 2 It changed the way they did art 3 It brought hope after the black death

Step-by-step explanation:

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer:

120 degrees is x

Step-by-step explanation:

because both are equal angles

btw nice Pikachu meme

Answer:

5)

$332.19

6)

$16,857.36

7)

$248.91

Step-by-step explanation:

monthly premium = Base Rate * \(\frac{Monthly Payroll}{100}\)

5)

given:

Base rate = $2.24
Monthly payroll = $14,830.00

unknown = monthly premium

 \(2.24 * \frac{14,830.00}{100}\) = $332.192≈$332.19

6)

given:

Base rate = $19.89
Monthly payroll = $84,752.96

unknown = monthly premium

\(19.89 * \frac{84,752.96}{100}\) = $16,857.364≈$16,857.36

7)

given:

Base rate = $2.90
Monthly payroll = $8,582.94

unknown = monthly premium

\(2.90 * \frac{8,582.94}{100}\)=$248.90526≈$248.91

2 1/2 teaspoons are needed for every 5 cups of flour from the ratio.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, A cookie recipe states for every 3 cups of flour. 1 1/2 teaspoons of every vanilla are needed

Since,

for 3 cups vanilla needed = 1 1/2 teaspoon

for 3 cups vanilla needed = 3/2 teaspoon

So,

for 1 cups vanilla needed = 1/2 teaspoon

Thus,

for 5 cups vanilla needed = 5/2 teaspoon

for 5 cups vanilla needed = 2 1/2 teaspoon

therefore, 2 1/2 teaspoons are needed for every 5 cups of flour.

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Answer:

\(x=5\)

Step-by-step explanation:

The perimeter of a figure is the sum of all its sides.

The sides are x, (x+3), and (2x). The perimeter is 23, so the sum of the expression equates to 23. Thus:

\(x+(x+3)+(2x)=23\)

Combine like terms:

\(4x+3=23\)

Subtract 3 from both sides:

\(4x=20\)

Divide both sides by 4:"

\(x=5\)

And we're done!

Answer:

The answer to the question is a rectangle.

Step-by-step explanation:

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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The numeric values for the function are given as follows:

a) f(-5) = 14.

b) f(0) = 10.

c) f(5/2) = 8.

d) f(5a) = -4a + 10.

e) f(5a - 15) = -4a + 22.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the function is given by:

f(x) = -0.8x + 10.

Hence the numeric values are given as follows:

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Answer:

0.7

Step-by-step explanation:

This one is simply pretty easy. the 7 in this is in the tenths place, and the 1 in this is in the hundredths place

Answer:

There's going to be 3 thirds in one whole sandwich. Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

9²/9⁷ = 9⁽²⁻⁷⁾ = 9⁻⁵ = 1/9⁵ = 1 / 59049

Answer:

With polar coordinates this isn’t true. In polar coordinates there is literally an infinite number of coordinates for a given point. For instance, the following four points are all coordinates for the same point. Here is a sketch of the angles used in these four sets of coordinates.

Step-by-step explanation:

Answer:

6.10 for 1 and 4.50 . for 2

Step-by-step explanation:

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Answer:

  see attached for a sketch

  area = 5 1/3 square units

Step-by-step explanation:

You want the area under the square root curve, above y=0, from x=0 to x=4.

The area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...

  dA = (√x)dx

  A = ∫(√x)dx

The power rule can be used for the integration:

  \(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)

The area of the region is 5 1/3 square units.

__

Additional comment

You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.

This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.

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The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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