1- If you ran 12 laps around the track in 4 minutes, what is the unit rate? 2- Lin bought 3 hats for $22.50. At this rateis this rught

The value of x which will make the provided triangles similar by the sss similarity theorem is 77.

The SSS similarity theorem is the theorem which is used to check the two triangle are similar or not.

SSS means the side-side-side. This theorem states that if all the three sides of a triangle are proportional to the three corresponding sides of the another triangle, then the triangles are similar.

In the given image, the sides of the first triangle are 35,20 and 20. The sides of the second triangle are x, 44,44.

Thus, by the SSS similarity theorem,

\(\dfrac{x}{35}=\dfrac{44}{20}\\x=\dfrac{44\times35}{20}\\x=77\)

The value of x which will make the provided triangles similar by the sss similarity theorem is 77.

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Answer:

77

Step-by-step explanation:

Each installment will be approximately $15,280.55.

To calculate the equal six-monthly installment, we can use the formula for the present value of an annuity.

Principal amount (P) = $500,000

Interest rate (r) = 12% per annum = 12/100 = 0.12 (compounded monthly)

Number of periods (n) = 20 (since there are 20 equal six-monthly installments)

The formula for the present value of an annuity is:

\(P = A * (1 - (1 + r)^(-n)) / r\)

Where:

P = Principal amount

A = Equal installment amount

r = Interest rate per period

n = Number of periods

Substituting the given values into the formula, we have:

$500,000 = \(A * (1 - (1 + 0.12/12)^(-20)) / (0.12/12)\)

Simplifying the equation:

$500,000 = A * (1 - (1.01)^(-20)) / (0.01)

$500,000 = A * (1 - 0.6726) / 0.01

$500,000 = A * 0.3274 / 0.01

$500,000 = A * 32.74

Dividing both sides by 32.74:

A = $500,000 / 32.74

A ≈ $15,280.55

Therefore, each installment will be approximately $15,280.55.

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Answer: The variables h and k in the general formula for a cube root function affect the graph by causing a horizontal and vertical shift, respectively. The value of h determines the horizontal position of the graph by shifting it to the right or left along the x-axis. If h is positive, the graph will shift to the right, and if h is negative, the graph will shift to the left. On the other hand, the value of k determines the vertical position of the graph by shifting it up or down along the y-axis. If k is positive, the graph will shift upward, and if k is negative, the graph will shift downward. It is important to note that these shifts do not affect the shape of the graph, only its position on the coordinate plane. Therefore, changing the values of h and k in the general formula for a cube root function will cause the graph to shift, but the overall shape of the graph will remain the same.

Step-by-step explanation:

The test statistic for the test is approximately 7.997

the critical value cutoff for the rejection region is approximately 9.210.

The null hypothesis for this test is typically formulated based on the advertiser's claim. In this case, the null hypothesis (H0) can be stated as follows:

H0: The proportions of people who stream their TV, have cable, and do not watch TV are equal to the claimed proportions of 70%, 25%, and 5%, respectively.

The alternative hypothesis (Ha) would be the complementary hypothesis, stating that at least one of the proportions is different from the claimed values.

To perform a hypothesis test, we can use the chi-square test of independence. The test statistic can be calculated as follows:

χ² = Σ((O - E)² / E),

where O represents the observed frequencies and E represents the expected frequencies.

Given the observed frequencies from the sample: stream = 32, cable = 10, no TV = 8, we need to calculate the expected frequencies based on the claimed proportions.

Expected frequencies:

Expected stream = (70% * 50) = 35,

Expected cable = (25% * 50) = 12.5,

Expected no TV = (5% * 50) = 2.5.

Now we can calculate the test statistic:

χ² = ((32 - 35)² / 35) + ((10 - 12.5)² / 12.5) + ((8 - 2.5)² / 2.5).

Calculating each term:

χ² = (9 / 35) + (4.5 / 12.5) + (18.45 / 2.5).

Summing up the terms:

χ² ≈ 0.257 + 0.36 + 7.38 ≈ 7.997.

The test statistic for the test is approximately 7.997 (rounded to three decimals).

To find the critical value cutoff for the rejection region, we need to refer to the chi-square distribution table with the appropriate degrees of freedom. In this case, since we have three categories (stream, cable, no TV), the degrees of freedom would be (number of categories - 1) = (3 - 1) = 2.

With an alpha level of 0.005, we need to find the chi-square value that corresponds to a cumulative probability of 1 - alpha = 0.995 with 2 degrees of freedom.

From the chi-square distribution table, the critical value is approximately 9.210.

Therefore, the critical value cutoff for the rejection region is approximately 9.210.

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Answer:

Vertex: (-5,-4) Y-int: (0,21) X-int. = (-7,0), (-3,0)

Step-by-step explanation:

The percentage of the seats in the theater were filled by the 6th graders on the trip is 78%.

Percentage is a measure of frequency that is expressed as the fraction of a number out of 100.

The percentage of the seats in the theater were filled by the 6th graders = (number of filled seats / total number of seats) x 100

(2496/3200) x 100 = 78%

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Answer:

None of these choices are correct.

Step-by-step explanation:

75 = perimeter

To find the total number of different routes from town A to town C, we can first find the number of different routes from A to B and then multiply it by the number of different routes from B to C. There are 7 different roads between A and B and 4 different roads between B and C. Therefore, the total number of different routes from A to C is 7 x 4 = 28.

(b) To find the total number of different routes from town A to town C and back, we can use the product rule. There are 28 different routes from A to C (as calculated in part a) and 28 different routes from C to A (since we can use any road once in each direction). Therefore, the total number of different routes from A to C and back is 28 x 28 = 784.

(c) To find the total number of different routes from town A to town C and back in part (b) that visit town B at least once, we can use the principle of inclusion-exclusion. There are 28 different routes from A to C and 28 different routes from C to A. However, we need to subtract the routes that do not visit B at all. To find this number, we can use the product rule again, since there are 5 different roads between A and C that do not go through B (2 from A to C and 3 from C to A). Therefore, the number of routes that do not visit B at all is 2 x 3 = 6. So, the total number of different routes from A to C and back in part (b) that visit B at least once is 28 x 28 - 6 = 784 - 6 = 778.

(d) To find the total number of different routes from town A to town C and back in part (b) that do not use any road twice, we can use the principle of permutations. Since we cannot use any road twice, we need to find the number of permutations of the roads. There are 7 roads between A and B, 4 roads between B and C, and 2 roads between A and C. Therefore, the total number of different routes from A to C and back in part (b) that do not use any road twice is 7P2 x 4P2 x 2P2 = 126 x 12 x 2 = 3024.

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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This looks like a quadratic equation!

Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

Answer: Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

wich is -0.4375

Step-by-step explanation:

The set of the first four Hermite polynomials is linearly independent and has exactly 4 elements, it automatically forms a basis for P3. Therefore, theorem D is the relevant theorem to use in this context.

To show that the first four Hermite polynomials form a basis of P3 (the vector space of polynomials of degree at most 3), we can use theorem D:D. Let V be a p-dimensional vector space, p≥ 1. Any linearly independent set of exactly p elements in V is automatically a basis for V.

In this case, the vector space is P3, which has a dimension of 4 since it consists of polynomials of degree at most 3. The first four Hermite polynomials provided (1, 2t, −2+4t², and -12t+8t³) form a linearly independent set since they are distinct polynomials and no polynomial can be expressed as a linear combination of the others.

Since the set of the first four Hermite polynomials is linearly independent and has exactly 4 elements, it automatically forms a basis for P3. Therefore, theorem D is the relevant theorem to use in this context.

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Answer:

C: ratio of the horizontal change to the vertical change of a line

Step-by-step explanation:

A and B are correct.

C is incorrect.

When doing a single sample t-test using SPSS, the constant is called the Test Value.

Test Value is in a One Sample t-Test, the test variable's mean is compared against a "test value", which is a known or hypothesized value of the mean in the population. Test values may come from a literature review, a trusted research organization, legal requirements, or industry standards.

\((\bar{\text{x}}-\mu)\div\dfrac{\text{s}}{\sqrt{\text{n}}}\)

In case statistics of two samples are to be compared, then a two-sample t-test is to be used, and its formula is expressed using respective sample means, sample standard deviations, and sample sizes. Mathematically, it is represented as, s2 = Standard Deviation of 2nd Sample.

Thus, When doing a single sample t-test using SPSS, the constant is called the Test Value.

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Answer:

4

Step-by-step explanation:

26x+6 - 12x +2 = 14x +4

60-4 = 56

56/14=4

Answer:

S = -90t + 550

Step-by-step explanation:

First we must note a few key things the question tells us:

1. The tickets sell at a constant rate, thus implying a linear relationship.

2. Tickets start selling at 10

3. The independent variable (t) is in hours after 10

4. The number of tickets (S) is declining, thus we should expect a negative gradient.

5. The number of tickets is our dependent variable since it is reliant on time.

y = mx+c is our general linear expression which we will call "Eq 0"

Lets substitute our knowns into this to find m and c. We know that "t" is independent and that "S" is dependent on "t" therefore, we know that our x-axis will be representing values for "t" and that our y-axis will represent values for "S"

We must use simultaneous equations to find m and c

Eq 1: 550 = m(0) + c -> 550 = c

Eq 2: 280 = m(3) + c -> 280 = 3m + c

From Eq 1. we already know that our y intercept is at 550.

To find our gradient, we must substitute our known (550 being the y-intercept) into the next equation.

Thus,

280 = 3m + 550

To isolate our variable (m) we subtract both sides by 550

280 - 550 = 3m + 550 - 550

-270 = 3m

To finally find m, we divide both sides by 3

-270/3 = 3m/3

-90 = m

Now we substitue both our knows into Eq 0, note that our gradient (m) is negative as expected.

y = -90x + 550

Or, in terms of S and t

S = -90t + 550

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

In a right triangle, if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, the length of the altitude is the geometric mean of the lengths of the two segments.

According to this

Which is the fourth option.

Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.

A fractional value is a value that represents a portion or part of the total value.

Fractional values can be depicted as proper, improper, or complex fractions.  They can also be depicted as decimals or percentages.

The remaining quantity of the shell pile = ³/₄

The quantity sorted by Terrence = ⁴/₆

The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%

Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.

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The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

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Answer:

answer is 5 hope it helps

Answer:

5

is the square root of \(\sqrt{25}\)

Step-by-step explanation:

\(\sqrt{25} = 5\\\)

The shape of the cross section is a triangle. It is always triangle if the triangular pyramid sliced from any side perpendicularly to its base. See the picture in the attachment!

A pyramid is a polyhedron that has one base and lateral faces with the vertex at the top of the pyramid. The shape of lateral faces is always a triangle. While, the shape of the base varies and is used to name the pyramid.

A triangular pyramid is a pyramid with a triangular base. It has three lateral faces.

If a triangular pyramid is sliced by a plane from any side that is perpendicular to its base, the cross section formed will be a triangle. One line is at the base and two lines are at the lateral faces. See the picture in the attachment!

Hence, the cross section formed by the slicing is a triangle.

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The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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The algebraic expression that can be represented by the statement is -5x/2 = 10

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

The negation of the product of five times a number divided by two is ten

Represent the variable with y

So, we have the following representation

The negation of the product of five times x divided by two is ten

Express the product as an actual product

So, we have the following representation

The negation of 5x divided by two is ten

Express the quotient as an actual quotient

So, we have the following representation

The negation of the 5x/2 is ten

Lastly, we have

-5x/2 = 10

Hence, the expression is -5x/2 = 10

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if its a word doc i dont know pdf search title at top. if not try the questions on go0gle

Step-by-step explanation:

Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.

What is a geometric progression?

A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.

We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.

From this, we get the common ratio to be 51/50 i.e. 1.02.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₈ = a₁ r⁽⁸⁻¹⁾

⇒a₈ = a₁ r⁷

⇒a₈ = 1500 (1.02)⁷

⇒a₈ = 1500 (1.1487)

⇒a₈ = $1723.05

Hence, Leo's balance after 8 months will be $1723.05.

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1)

The area of the electronic board on the scale drawing is 1800 cm².

2)

Using the scale factor 5:1.

Length:

1 = 50

5 = 250 cm

Width:

1 = 36 cm

5 = 180 cm

3)

The area of the actual electronic board is 45000 cm²

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Scale factor = 5 : 1

Now,

Electronic board dimensions:

Length = 50 cm

Width = 36 cm

Now,

Area of the electronic board on the scale drawing.

= length x width

= 50 x 36

= 1800 cm²

Now,

Actual dimensions:

Length = 250 cm _____(1)

Width = 180 cm _____(2)

Using the scale factor 5:1.

1 = 50

5 = 250 cm

And,

1 = 36 cm

5 = 180 cm

Area of the actual electronic board.

From (1) and (2)

= 250 x 180

= 45000 cm²

Thus,

The area of the electronic board on the scale drawing is 1800 cm².

The area of the actual electronic board is 45000 cm²

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Given:

The area of a sector, A=74.84 sq. in.

The radius of the sector, r=8 in.

Now, the expression for the area of a sector can be written as,

Here, θ is the central angle in degrees.

Rearrange the above equation and substitute values to find the angle θ.

Answer:

It's a trick question, there is none

Step-by-step explanation:

Based on the provided graph, the correct statement is that nearly "200 of the cancer cases reported in the U.S. are attributable to smoking".

The graph visually represents statistical data or relationships between variables by drawing lines or bars that connect data points or present information in a graphical format. In this case, the graph likely shows the attribution of cancer cases to smoking in the U.S.

Smoking is a dangerous practice that is known to be one of the leading causes of cancer worldwide. The link between smoking and cancer is well-established, with tobacco smoke containing various harmful chemicals that can damage DNA and increase the risk of developing cancer. It is estimated that nearly 25% of all cancer cases can be attributed to smoking.

The graph likely presents data indicating the number of cancer cases attributable to smoking in the U.S. Based on the information provided, the graph suggests that nearly 200 cancer cases in the U.S. can be directly linked to smoking.

Therefore, the correct statement is that nearly 200 of the cancer cases reported in the U.S. are attributable to smoking.

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