5(x −1) < 3x + 10 − 8x

Step-by-step explanation:

Do

(4÷2×5)

first

.............

Answer: 5xy

Step-by-step explanation:

Answer: -8 and 4 or 16 and 2

Step-by-step explanation:

A pair of integers that satisfies the given conditions is -8 and 4.

When multiplied, the product of -8 and 4 is -32. When added, the sum of -8 and 4 is -4. Therefore, -8 and 4 are a pair of integers that satisfies the given conditions.

To verify this solution, we can multiply -8 and 4 to get -32, and then add -8 and 4 to get -4. This confirms that -8 and 4 are a valid solution to the problem.

It is also possible to find other pairs of integers that satisfy the given conditions. For example, another pair of integers that satisfies the given conditions is -16 and 2. When multiplied, the product of -16 and 2 is -32. When added, the sum of -16 and 2 is -4. Therefore, -16 and 2 are another pair of integers that satisfies the given conditions.

Answer:

0.56

it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%

Answer:

15min : 4 3/4 laps

30min : 9 2/4 laps

45min: 14 1/4 laps

60min: 20 laps

Step-by-step explanation:

Answer:

Area = 1725 ft²

Step-by-step explanation:

In this question, we have to calculate the area of the trapezoid. As mentioned in the hint, the formula for the area of a trapezoid is:

\(\boxed{\mathrm{Area = \frac{b_1 + b_2}{2} \times h}}\),

where \(\mathrm {b_1}\) and \(\mathrm {b_2}\) are the two parallel bases of the trapezoid, and h is the height of the trapezoid.

As we can see in the diagram the two bases are 50 ft and 65 ft respectively, and the height is 30 ft. Using this information and the formula above, we can calculate the formula of the trapezoid:

\(\mathrm{Area = \frac{(50 + 65)\: \mathrm{ft}}{2} \times 30 \: \mathrm{ft}}\)

        \(= \frac{115 \: \mathrm {ft}}{2} \times 30 \: \mathrm{ft}\)

        \(= \bf 1725 \: ft^2\)

Therefore, the area of the lawn is 1725 ft².

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

(x+6)*(x+2)

step-by-step explanation:

Answer:

b.) 5.385

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

(3, 9 )

Step-by-step explanation:

x + y = 12 → (1)

y = 3x → (2)

substitute y = 3x into (1)

x + 3x = 12

4x = 12 ( divide both sides by 4 )

x = 3

substitute x = 3 into (2) and solve for y

y = 3x = 3 × 3 = 9

solution is (3, 9 )

Answer:

its 2/5

Step-by-step explanation:

What is Start Fraction 4 Over 5 End Fraction divided by one-third A fraction bar you may ask? The top bar is labeled 1.3 bars underneath the bars are labeled one-third. So, 5 bars underneath the 4 bars are labeled one-fifth. And 15 bars underneath the 5 bars are labeled Start Fraction 1 Over 15 End Fraction. The quotient is ??? well it would be 2 and all you have to do is figure it out so the answer is below.

Well, the correct fraction would be 2 and 2/5 because this is what the model shows.

\({Answer}\)

Considering ΔADE and ΔACB as similar triangles, the distance across the lake is, DE = 107.1 ft.

The image shows two similar triangles, ΔADE and ΔACB. Therefore:

AD/AC = DE/CB

75/(75 + 100) = DE/250

75/175 = DE/250

DE = 107.1 ft

Therefore, considering ΔADE and ΔACB as similar triangles, the distance across the lake is, DE = 107.1 ft.

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Answer:

Solution given:

The length of the garden[l] = 24 3/4 =99/4feet.

breadth or width [b]=b

perimeter of his garden = 70 1/2=141/2 feet.

2[l+b]=141/2ft

99/4+b=141/4

b=141/4-99/4

b=21/2

b=10 ½ft

So the width of the garden is 10 ½ft.

Question is incomplete. Here is the complete question.

A city employee paints curbs iin parking lots and replaces road signs. It takes 0.5 hour to paint a parking lot curb and 2.5 hours to replace a road sign. The function below can be used to find c, the number of parking lot curbs the employee paints when he replaces r road signs in a 40-hour workweek.

\(c=\frac{40-2.5r}{0.5}\)

If the employee painted 20 curbs in one week, how many road signs did he replace that week?

a) 20    b) 30    c) 0     d) 12

Answer: d) 12

Step-by-step explanation: In one week, the employee painted 20 curbs.

c is the number of curbs painted in one week, so: c = 20

\(20=\frac{40-2.5r}{0.5}\)

\(40-2.5r=20*0.5\)

\(-2.5r=10-40\)

\(-2.5r=-30\)

\(r=\frac{-30}{-2.5}\)

r = 12

In one week, the employee replaced 12 road signs.

Answer:

DOnt know

Step-by-step explanation:

dont know

Answer:

Is this Algebra?

Step-by-step explanation:

The probability that both randomly chosen people own a dog can be calculated using the concept of independent events. If 18% of people own dogs, it means that the probability of a person owning a dog is 0.18.

When picking the first person, there is a 0.18 probability that they own a dog. Now, assuming replacement (putting the person back before picking the second person), the probability that the second person also owns a dog is also 0.18.

To find the probability of both events occurring, we multiply the individual probabilities together: 0.18 * 0.18 = 0.0324.

Therefore, the probability that both randomly chosen people own a dog is 0.0324, which is equivalent to 3.24%. This means that if we were to repeat this random selection process many times, we would expect approximately 3.24% of the time to end up with two dog owners.

It's important to note that this calculation assumes independence between the events and replacement, meaning the probability of one person owning a dog does not affect the probability of the other person owning a dog.

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The values are used to calculate the confidence interval for the population mean when the population standard deviation is not known, and the sample size is small.

a. For a 95% confidence level and a sample of 8 observations, the degrees of freedom (df) would be 8 - 1 = 7. Looking up the value in the t-table with 7 degrees of freedom and a significance level of α/2 = 0.025 (since it's a two-tailed test), we find tα/2,df = 2.365.

b. For a 90% confidence level and a sample of 8 observations, the degrees of freedom (df) would still be 7. Using the t-table with 7 degrees of freedom and a significance level of α/2 = 0.05 (since it's a two-tailed test), we find tα/2,df = 1.895.

c. For a 95% confidence level and a sample of 28 observations, the degrees of freedom (df) would be 28 - 1 = 27. Using the t-table with 27 degrees of freedom and a significance level of α/2 = 0.025, we find tα/2,df = 2.056.

d. For a 90% confidence level and a sample of 28 observations, the degrees of freedom (df) would still be 27. Using the t-table with 27 degrees of freedom and a significance level of α/2 = 0.05, we find tα/2,df = 1.703.

The values of tα/2,df are as follows:

a. tα/2,7 = 2.365

b. tα/2,7 = 1.895

c. tα/2,27 = 2.056

d. tα/2,27 = 1.703

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Answer:

AB and CD are parallel

Step-by-step explanation:

AB has the slope of -2/5

lets see what slope the line CD has:

as we see AB and CD have same slope, therefore they are parallel

Answer:

Mansah obtained 150 mark out of 240 mark in an English test .what was her percentage score

The optimal design for a cylindrical can with a lid to hold 2 liters of water minimizes the amount of metal used.

To design a cylindrical can with a lid that can contain 2 liters (2000 cm³) of water while minimizing the amount of metal used, we need to optimize the dimensions of the can. Let's denote the radius of the base as r and the height as h.

The volume of a cylindrical can is given by V = πr²h. We need to find the values of r and h that satisfy the volume constraint while minimizing the surface area, which represents the amount of metal used.

Using the volume constraint, we can express h in terms of r: h = (2000 cm³) / (πr²).

The surface area A of the cylindrical can, including the lid, is given by A = 2πr² + 2πrh.

By substituting the expression for h into the equation for A, we can obtain A as a function of r.

Next, we can minimize A by taking the derivative with respect to r and setting it equal to zero, finding the critical points.

Solving for r and plugging it back into the equation for h, we can determine the optimal dimensions that minimize the amount of metal used.

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Answer: y=1/3x-2

Step-by-step explanation:

y=Mx+b

1/3 is rise over run

-2 is the y intercept

Answer:

I think B

Step-by-step explanation:

because their age group is 20-25 more of a constant age group

compared to 20-30

We can say that equation (C) [1430p + 2200 = -4001] is equivalent to the given equation [1.43p + 2.2 = -4.001].

So, the equivalent expression is:

Let us take the number with the most numbers after decimals, that is -4.001.

Now, if we -4.001 × 1000, then we obtain:

This means we will multiply all terms with 1000 as follows:

Therefore, we can say that equation (C) [1430p + 2200 = -4001] is equivalent to the given equation [1.43p + 2.2 = -4.001].

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To find the determinant using elementary row or column operations, we can use the following steps:

1. Rewrite the matrix in an augmented form with the identity matrix on the right:

3 -3 -2 | 1 0 0
3 1 2 | 0 1 0
-6 6 4 | 0 0 1

2. Use elementary row operations to transform the matrix into an upper triangular form:

R2 = R2 - R1
R3 = R3 + 2R1
R3 = R3 + 2R2

3 -3 -2 | 1 0 0
0 4 4 | -1 1 0
0 0 0 | -2 2 1

3. The determinant of an upper triangular matrix is the product of its diagonal elements:

det(A) = 3 x 4 x 0 = 0

Therefore, the determinant of the original matrix is 0.

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Answer: D

Step-by-step explanation:

The expression is simplified to 2/3x²y⁻³

Index forms are described as mathematical forms of writing numbers that are too large or small in more convenient forms.

Other names for index forms are scientific notation and standard forms.

The rules of index forms are;

From the information given, we have that;

8x⁵y/12x³y⁴

Divide the values

2/3 x⁵⁻³y¹⁻⁴

Subtract the exponents

2/3x²y⁻³

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