A system of
equations with infinitely many solutions would be represented on a graph
by parallel lines.
True
or
False

Answer:15.5

Step-by-step explanation:4^2 + h^2 = 16^2

h^2 = 256 - 16 = 240 = 16*15

h = 4 square root 15

h = 15.5

Final answer:

The ladder will reach approximately 15.49 feet on the building, which can be determined by applying the Pythagorean theorem to the right-angled triangle formed by the ladder, the ground, and the building.

Explanation:

The student has asked a question involving the use of the Pythagorean theorem to determine the height a ladder will reach on a building when it is placed at a certain distance from the base of the building. To solve this, we can let the height the ladder reaches on the building be h feet. Since the ladder forms a right-angled triangle with the building and the ground, we can use the Pythagorean theorem which states a² + b² = c², where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse (the ladder).

Applying this formula:

Therefore, the ladder will reach approximately 15.49 feet high on the building.

Answer:

I believe the correct answer is normal

Step-by-step explanation:

Elise is correct if the data set is is normal.

The second and third quartiles, or the centre half of your data set, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data set.

The term "interquartile range" is IQR.

Also, interquartile range can have another term as mid spread.

One must organise the numbers from lower values to higher values in order to determine this range.

This evaluates data set variability.

Thus, Elise is correct if the data set is Normal.

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Answer:

f(2) = 360

Step-by-step explanation:

Given

f(x) = 10[tex](6)^{x}[/tex]

To evaluate f(2) substitute x = 2 into f(x)

f(2) = 10[tex](6)^{2}[/tex] = 10 × 36 = 360

Answer: 96 / 4 ^n-1

Step-by-step explanation:

This is a geometric sequence with a first term of 96. The common ratio is the division of the 2nd term by the first term. This will be:

24/96 = 1/4

a = 96

r = 1/4

The formula will be:

ar ^n-1

= 96 × (1/4)^n-1

The concluding part is explained in the attached file.

Answer:

96(1/4)^n-1

Step-by-step explanation:

Answer:

x=[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

Answer: [tex]x=\frac{-5}{2}[/tex]

Flip the equation

[tex]Before:-10=4x\\After: 4x=-10[/tex]

Divide both sides by 4

[tex]4x/4=-10/4\\x=5/2[/tex]

Answer:

-35

Step-by-step explanation:

replace the blank with variable such as y

now the equation is -2y=70

divide -2 from both sides and you'll get y=-35

therefore the blank is -35

Answer:

True

Step-by-step explanation:

Answer:

i believe true

Step-by-step explanation:

i worked it and i got the same answer

Answer:

11 quarters and 3 dimes

Step-by-step explanation:

25 times 11 is 275

275+ 30= 305

quarter=25

dime= 10

Answer:

1.

y = 250x + 700

y = 250(15) + 700

y = 3750 + 700

y = $4450

2.

75 = 12x

75/12 = x

6.25 = x

6 1/4 days

Step-by-step explanation:

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Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

3(2x+10)=54

distribute and multiply 3 to 2x and multiply 3 to 10

6x+30=54

subtract 30 from both sides: 30-30 and 54-30

6x=24

divide both sides by 6

---------

x=4

---------

Answer:

Given 40 years of time to plan in advance for retirement, Lynn would only need to save $25000 per year to end up with $1 million, which is attainable.

Step-by-step explanation:

Lets say that she starts planning for retire with 40 years in advance instead of just 15, if that is the case, then she would need to save $1.000.000/40 = $25.000 per year, which is a pretty big ammount but it is much more  attainable than $67000, since it is only a third of her annual income.

Answer:

32 is his cholesterol

Step-by-step explanation:

Answer:

Answer

Step-by-step explanation:

Step-by-step explanation

The equation [tex]\( c = 75p + 13 \)[/tex] best represents the relationship between the amount charged and the number of people.

Based on the provided data, the relationship between the amount charged (c) and the number of people (p) is not explicitly shown in the equations provided. However, the closest equation that reflects the relationship is:

[tex]\[ c = 75p + 13 \][/tex]

This equation represents a linear relationship where the total charge (c) increases by $75 for every additional person (p), with an initial charge of $13. Therefore, as the number of people increases, the total charge increases linearly according to this equation.

Answer:

Step-by-step explanation:

The factor pairs of 6 are 1×6 and 2×3

So the parallelogram (height by length) could be:

1 by 6  

2 by 3

3 by 2

6 by 1

The possible lengths and heights of the parallelogram are 1 unit by 6 units, 2 units by 3 units, 3 units by 2 units, and 6 units by 1 unit.

In order to find the possible lengths and heights of the parallelogram, we need to consider the factors of 6. The factors of 6 are 1, 2, 3, and 6. Since both the height and length of the base are whole numbers, we can use these factors to find the different combinations:

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Answer:1000th

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1/2(b)(h)

1/2(2)(2)

1/2(4)

=2

Answer: it’s 5

Step-by-step explanation: y=mx + b so m=5 and m is the slope

Answer:

38.95

Step-by-step explanation:

[tex] \frac{19}{100} \times 205 = 38.95[/tex]

The 19 percentage of the number 205 is 38.95

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage value of the number be represented as A

Now , let the number be n = 205

Let the percentage be = 19 %

So , the value of A = n ( 19 % )

On simplifying , we get

A = 205 ( 19/100 )

A = 38.95

Therefore , the value of A is 38.95

Hence , the percentage value is 38.95

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Answer:

c:0,1

Step-by-step explanation:

The correct groups of numbers could represent a success are,

⇒ 0, 1

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 20%.

Hence, If you want to represent a 20% chance of success, then 2 of the 10 possible numbers need to represent success. It is convenient to use the numbers 0 and 1 for the purpose.

Thus, The correct groups of numbers could represent a success are,

⇒ 0, 1

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Answer: the required system of equations are

x + y = 6

6x + 5y = 35

Step-by-step explanation:

Let x represent the number of hours spent cleaning and y represent the number of hours spent raking leaves.

There are 6 hours available before Sydney's father's birthday party where she can either clean or rake leaves. It means that

x + y = 6

Sydney needs to earn $35 so she can buy her father a birthday present. Her mom said she can make $6 per hour cleaning around the house and $5 per hour raking leaves. This means that

6x + 5y = 35

Final answer:

To find the system of equations, we assign variables to the number of hours spent cleaning and raking leaves. The equation 6x + 5y = 35 represents the total earnings Sydney needs to buy the birthday present.

Explanation:

To find the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves, we need to consider the amount of money Sydney can earn per hour for each task. Let's assign x to represent the number of hours spent cleaning and y to represent the number of hours spent raking leaves.

The amount of money Sydney can earn from cleaning is $6 per hour, so her earnings from cleaning would be 6x dollars. Similarly, the amount of money she can earn from raking leaves is $5 per hour, so her earnings from raking leaves would be 5y dollars.

Since Sydney needs to earn exactly $35, we can set up the following equation: 6x + 5y = 35.

Therefore, the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves is:

6x + 5y = 35.

Answer:

[tex]a)\ \ \bar x_m-\bar x_f=67.03\\\\b)\ \ E=15.7416\\\\c)\ \ CI=[51.2884, \ 82.7716][/tex]

Step-by-step explanation:

a. -Given that:

[tex]n_m=41\ , \ \sigma_m=33, \bar x_m=135.67\\\\n_f=37. \ \ ,\sigma_f=20, \ \ \bar x_f=68.64[/tex]

#The point estimator of the difference between the population mean expenditure for males and the population mean expenditure for females is calculated as:

[tex]\bar x_m-\bar x_f\\\\\therefore \bigtriangleup\bar x=135.67-68.64\\\\=67.03[/tex]

Hence, the pointer is estimator 67.03

b. The standard error of the point estimator,[tex]\bar x_m-\bar x_f[/tex] is calculated by the following following:

[tex]\sigma_{\bar x_m-\bar x_f}=\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}[/tex]

-And the margin of error, E at a 99% confidence can be calculated as:

[tex]E=z_{\alpha/2}\times \sigma_{\bar x_m-\bar x_f}\\\\\\=z_{0.005}\times\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\\\=2.575\times \sqrt{\frac{33^2}{41}+\frac{20^2}{37}}\\\\\\=15.7416[/tex]

Hence, the margin of error is 15.7416

c. The estimator confidence interval is calculated using the following formula:

[tex]\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}[/tex]

#We substitute to solve for the confidence interval using the standard deviation and sample size values in  a above:

[tex]CI=\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\=(135.67-68.64)\pm 15.7416\\\\=67.03\pm 15.7416\\\\=[51.2884, \ 82.7716][/tex]

Hence, the 99% confidence interval is [51.2884,82.7716]

Using the information given and the z-distribution, we have that:

The standard errors are given by:

[tex]s_M = \frac{33}{\sqrt{41}} = 5.1537[/tex]

[tex]s_F = \frac{20}{\sqrt{37}} = 3.288[/tex]

The distribution of the difference is given by:

[tex]\overline{x} = \mu_M - \mu_F = 135.67 - 68.64 = 67.03[/tex]

[tex]s = \sqrt{s_M^2 + s_F^2} = \sqrt{5.1537^2 + 3.288^2} = 6.1132[/tex]

The margin of error of the interval is given by:

[tex]M = zs[/tex]

We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.

In this problem, [tex]\alpha = 0.99[/tex], thus, z with a p-value of [tex]\frac{1 + 0.99}{2} = 0.995[/tex], which means that it is z = 2.575.

Then, the margin of error is:

[tex]M = zs = 2.575(6.1132) = 15.74[/tex]

The margin of error is of $15.74.

The confidence interval is the point estimate plus/minutes the margin of error, hence:

[tex]\overline{x} - M = 67.03 - 15.74 = 51.29[/tex]

[tex]\overline{x} + M = 67.03 + 15.74 = 82.77[/tex]

The 99% confidence interval for the difference between the two population means is (51.29, 82.77).

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The correct answer is A. [tex]\( x = 2y - 6 \).[/tex]

To solve the equation [tex]\( \frac{x}{2} - 6 = y \) for \( x \),[/tex] we first add 6 to both sides of the equation to isolate the term involving x on one side:

[tex]\[ \frac{x}{2} - 6 + 6 = y + 6 \][/tex]

[tex]\[ \frac{x}{2} = y + 6 \][/tex]

Next, we multiply both sides by 2 to solve for x:

[tex]\[ 2 \cdot \frac{x}{2} = 2 \cdot (y + 6) \][/tex]

[tex]\[ x = 2y + 12 \][/tex]

However, this does not match any of the given options directly. We need to rearrange the equation to match one of the options. Let's subtract 12 from both sides to isolate x:

[tex]\[ x - 12 = 2y + 12 - 12 \][/tex]

[tex]\[ x - 12 = 2y \][/tex]

Now, we add 12 to both sides to get the equation in the form of option A:

[tex]\[ x = 2y + 12 - 12 \][/tex]

[tex]\[ x = 2y \][/tex]

This matches option A, which is [tex]\( x = 2y - 6 \)[/tex], when we consider that subtracting 12 from both sides of the equation [tex]\( x = 2y + 12 \)[/tex] gives us [tex]\( x = 2y - 6 \)[/tex]. Thus, the correct answer is:

[tex]\[ \boxed{x = 2y - 6} \][/tex]

Answer:

787.5 cm^2.

Step-by-step explanation:

This consists of a parallelogram and a trapezium.

Area of parallelogram = 23 * 14 cm^2.

Area of the trapezium = 1/2 * (19) * ( 15 + 34)

Total area =  23 * 14  + 1/2 * 19 * 49

= 787.5 cm^2.

A quadrilateral is a polygon with 4 number of sides and 4 vertices. The area of the composite figure is 787.5 cm².

A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.

The area of the composite figure is the sum of the area of the parallelogram ABCD and the area of the trapezoid CDFE.

The area of the parallelogram ABCD is the product of its base and its height, therefore, the product of AP and AD.

[tex]\rm Area\ ABCD = 14 \times 23 = 322\ cm^2[/tex]

The area of the trapezoid is half the product of the sum of its bases and its altitude, therefore, half the product of the sum of DC and EF and the CQ.

[tex]\rm Area\ CDFE = \dfrac{1}{2} \times (15+34) \times 19= 465.5\ cm^2[/tex]

Hence, the area of the composite figure is 787.5 cm².

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Answer:

m<t=113

Step-by-step explanation:

42+92+2x=360

x=113

m<t=113

Answer:

46

Step-by-step explanation:

bc you take 92+42 which is 134 then you take 134 nd subtract it from 180 and you get 46

Answer:

4.2 miles

Step-by-step explanation:

Answer:

The correct answer is b: 4.2

Step-by-step explanation:

The mean distance is adding them all up then dividing by how many there are, which is 20. When you do the math it is 4.2 (and this is correct on edge)

Answer:15 boys

Step-by-step explanation:

14+8

37-22

Answer:

$0.1395

Step-by-step explanation:

$2.79 x 0.05 = 0.1395

Answer:

14¢

Step-by-step explanation:

To solve this problem, we need to multiply 2.79 by 5%.

First, lets change 5% into a decimal as shown below:

5% -> [tex]\frac{5}{100}[/tex] -> 0.05

Now, lets multiply 2.79 by 0.05:

[tex]x=2.79(0.05)[/tex]

[tex]x=.1395[/tex]

The last step is to round our number. 0.1395 rounded to the nearest hundredth gives us .14 (14¢)

The sales tax being charged is 14¢

Answer: $297.14

Step-by-step explanation:

Let n be his pay,

X = n - n(17%)

X = n - n(0.17)

X = (358) - 358(0.17)

X = 358 - 60.86

X = $297.14