One car travels 30 miles in the same amount of time it takes another car to travel 25 miles. If the second car travels fuse ante per hour slower, how fast does the first car travel?

The value of s, considering that quadrilateral DEFG is a rhombus, is given as follows:

s = 55.

To obtain the value of S, we must consider triangle CED, and the fact the sum of the measures of the internal angles of a triangle is of 180º.

The measures of the internal angles of triangle CED are given as follows:

As the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle E is given as follows:

90 + 60 + <E = 180

150 + <E = 180

<E = 30º.

As <E = s - 25, the value of s is obtained as follows:

s - 25 = 30

s = 30 + 25

s = 55.

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If a rhombus has an angle measure of 120 and it’s longer diagonal has a length of 10 inches. The area of the rhombus is 28.85.

Obtuse angle = 120 so, the other two angles must add up to 60 and each would be half of 60 or 30.

Hence,

Sin 30°  = 0.5  

Sin 60° = 0.86602540378

Now let find the length of breadth

Length of breadth  = 0.5 / 0.86602540378

Length of breadth = 0.577

Now let find the area using this formula

A =b × h

Where:

b=0.577

h=0.5

A = 0.577 x 0.5

A = 0.2885

A  = 28.85

Therefore the area is 28.85.

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By solving an inequality we will see that for 7 movies (or more) the first store is a better deal.

We know that the first store charges $12.50 as a fixed cost plus $1.50 per movie rented, so if you rent x movies, the total cost is:

c(x) = $12.50 + $1.50*x

While the second store charges $3.50 per movie, then the cost for renting x movies here is:

h(x) = $3.50*x

We want to find the minimum value x such that c(x) < h(x), then we need to solve the inequality:

$12.50 + $1.50*x <  $3.50*x

$12.50 < $3.50*x - $1.50*x

$12.50 < $2.00*x

$12.50/$2.00 < x

6.25 < x

So, for x = 7 the first store is a better deal.

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The equation of line p is y = ax + b then y = -2ax + b + 3 could be only the equation of line q out of the given options.

Therefore, the answer is C) y = -2ax + b + 3.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. So in case of line p, a is the slope and b is the y-intercept. Let equation of q by y = m'x + b'.

From the figure it is evident that line p has a positive slope while line q has a negative slope. So slope of q is negative of slope of line q multiplied by a positive constant, say c, then

m' = -2ac

From figure we can observe that y-intercept of p is 0 and q has a positive y-intercept, so

b' = b + k, k is a positive constant

So equation of q is y = -2acx + b + k, where c and k are positive constants. So only option C is of this format.

--The question is incomplete, answering to the question below--

"The equation of line p is y = ax + b. Which of these could be the equation of line q?

A. y = -2a(x + 3) + b

B. y = -2ax + b

C. y = -2ax + b + 3

D. y = -2ax + b - 3"

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Based on the provided information, a) bias is introduced through convenience sampling there could be specific variable associated with the first hundred students. It can be avoided by simple random sampling. b) bias is introduced through wording as it includes a negative consequence. It can be avoided by just asking for an opinion without any associated reasoning or consequences.

Bias refers to a deviation of feedback which is based on certain influences by the surveyor and respondent. Sampling bias or selection bias refers to a type of bias in which a researcher gathers a sample of respondents for a questionnaire that does not accurately represent the population. Survey bias refers to the way the question is phrased or formatted, leading people to choose a certain answer instead of another. In the given case,

a) A bias may have been introduced based on the way the convenience sample was selected as there could be specific variable associated with each of the first hundred students that walk into the dining room. The first hundred students could possibly like the food and that is the reason why they come early to the dining room. Selecting students at the dining room may also exclude the students who dislike the food and choose to eat elsewhere. A simple random sample can help avoid this bias. By randomly selecting students at the university campus would provide a more inclusive and true representation of the population.

b) A bias may have been introduced based on the way the question is worded is to maintain the current meal plan as it presents a negative consequence to introducing a new meal plan. It states that a new meal plan would result in more cost. In order to avoid bias, the survey should ask students opinion about the food without introducing any external reasoning.

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Answer:

3

Step-by-step explanation:

to find the rate you have to multiply the fraction so...

12 (the pages) times 1/4 (the hour) you get 3

Answer:

48 pages per hour; 3 hours per page

Step-by-step explanation:

A). You can find the unit rate for pages per hour by first multiplying the hours by its reciprocal, 4, which essentially becomes 1 hour and what you do to one side must be done to the other side, so multiplying 12 by 4 gets you 48 pages. Therefore,  Leo reads 48 pages per hour.

B). To find hours per page, you do the same thing, except that this time, you divide 12 on each side because you are trying to find the hours per page. 12 pages divided by 12 gets you 1 page and dividing 1/4 by 12 is the same thing as multiplying 1/4 by 12 since when dividing fractions with another fraction, the method is to use the reciprocal of the second fraction (in this case, 1/12 becomes 12) and you change the sign to its inverse and you simplify. A helpful acronym you can use is this. KEEP IT, CHANGE IT, FLIP IT . You keep the first fraction as it is, change the sign to its inverse, and flip the second fraction (virtually, the reciprocal). Therefore, in this case, it becomes 1/4 times 12 and 12 divided by 4 is nothing but 3.
Thus, Leo takes 3 hours to read each page.

Hope this helped! :D

The solution to the differential equation is y = 2x/(y + 2x), which can be interpreted as y is equal to twice x divided by y plus twice x.

du/dx = 2(y + x)

Integrating both sides, we get

∫du/2(y + x) = ∫dx

1/2 ∫u du = x + C

(1/2)u^2 = x + C

(1/2)(y + x)^2 = x + C

y^2 + 2xy + x^2 = 2x + C

y^2 + 2xy = 2x + C - x^2

y^2 + 2xy = 2x + C - x^2

y^2 + 2xy + C = 2x + C

y^2 + 2xy + C = 2x + C

y^2 + 2xy = 2x

y(y + 2x) = 2x

y = 2x/(y + 2x)

y = 2x/(y + 2x) y = 2x/(y + 2x), which can be interpreted as y is equal to twice x divided by y plus twice x.

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After 40 hours the population of bacteria will be equals to 318 hours.

We can calculate the total population growth using the following equation:

A(t)= A₀× 2ᵗ/¹⁵

Where, A(t) --> the total population

A₀ --> the initial population

t --> the time in hours

From the statement we know that the population of bacterias doubles every 15 hours, so, using the formula we have: A(15) = A₀ × 2ᵗ/¹⁵

The initial population is = 50 , then

A(15) = 50×2¹⁵/¹⁵ = 100

It shows that every 15 hours, the population of bacterias doubles it size. We are asked to calculate the popualation after 40 hours, so:

A(40) = 50 × 2⁴⁰/¹⁵

= 6.35 × 50 = 317.5 ~ 318

So, after 40hours the population of bacteria will be 318.

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The product of these two complex numbers is calculated by multiplying the real numbers and imaginary parts separately and then combining them, resulting in -25.

Step 1: Multiply the real parts: (-3i * 3i = -9i^2

Step 2: Multiply the imaginary parts: 4 * 4 = 16

Step 3: Combine the results: -9i^2 + 16 = -25

(-3i * 3i) + (4 * 4) = -9i^2 + 16 = -25

Complex numbers consist of two parts - a real part and an imaginary part. To find the product of two complex numbers, both the real and imaginary parts must be multiplied separately, and then the results combined. In this example, (-3i 4 and 3i 4), the real parts are multiplied together to get -9i2. The imaginary parts are multiplied together to get 16. These results are then combined to get the product of the complex numbers, which is -25. To complete the calculation, we must also take into account that the imaginary part is always multiplied by the coefficient i. This means that the result of the real part multiplication is -9i2, not just -9.

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The standard deviation is 5.94 and rounded to the nearest tenth, the standard deviation is 5.9.

The standard deviation from the mean is a measure of how spread out the data is in a set of numbers. It is calculated by finding the square root of the variance of the data set, which is the average of the squared differences between each data point and the mean.

To calculate the standard deviation from the mean for the set of numbers 4, 5, 6, 14, 15, and 5, you would first need to find the mean of the set by adding all of the numbers together and dividing by the number of numbers in the set. The mean of this set is 8.17.

Next, we will need to calculate the squared differences between each number and the mean, and then average those squared differences. The variance of this set is 35.15.

Finally, we will take the square root of the variance to find the standard deviation, which is approximately 5.94. Rounded to the nearest tenth, the standard deviation is 5.9.

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For the coordinates and their weights, the weight average is 5

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

Coordinates and weights

The coordinates and weights are then given as:

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

Substitute the known values in the above equation

So, we have the following equation

Weight average = (3 * 2 + 9 * 1)/(2 + 1)

Evaluate the product in the above equation

So, we have the following equation

Weight average = (6 + 9)/(2 + 1)

Evaluate the sum in the above equation

So, we have the following representation

Weight average = (15)/(3)

Evaluate the quotient in the above equation

So, we have the following equation

Weight average = 5

Hence, the weight average of the coordinates is 5

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The factored form of the equation -15w + 9wz - 6z + 10 is,

⇒ (3w - 2) (3z - 5)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ -15w + 9wz - 6z + 10

Now, Factor the equation as;

⇒ -15w + 9wz - 6z + 10

⇒ 3w (- 5 + 3z) - 2(3z - 5)

⇒ 3w (3z - 5) - 2 (3z - 5)

⇒ (3w - 2) (3z - 5)

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Answer:

-97290

Step-by-step explanation:

The system of inequalities of the scenario is x + y ≤ 24 and 6x + 5y ≥ 550

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

Using the above as a guide, we have the following:

Number of containers = x + y

Where

x = Yoghurt

y = Kefir

This means that

x + y = At most 24

Express as an inequality

x + y ≤ 24

For the earnings, we have:

6x + 5y = Total earnings

Express as an inequality

6x + 5y ≥ 550

Hence, the inequalities are x + y ≤ 24 and 6x + 5y ≥ 550

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Complete question

Nathaniel has enough goat's milk to make at most 24 containers of fermented milk product (either yogurt or kefir). Each container of yogurt sells for $6.00​​, while each container of kefir sells for $5.00 Nathaniel needs to make at least $550.

What is the system of inequalities of the scenario?

Answer:

The first image is right. The line on X = -1

Step-by-step explanation:

x + 2 ≥ 1

x ≥ 1 -2

x ≥ -1

By using Pythagorean theorem to find the length of the hypotenuse, we get the answer as hypotenuse of 115

A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the legs of the right triangle.

In a right triangle, the hypotenuse is the side that is opposite the right angle. It is the longest side of the triangle and it is always opposite the 90-degree angle. The other two sides of the right triangle are called the legs, and they form the right angle.

we can use the Pythagorean theorem to find the length of the hypotenuse:

a^2 + b^2 = c^2

82^2 + 80^2 = c^2

6724 + 6400 = c^2

c = √(6724 + 6400) = √13124

c = 114.74

Since all three sides of the triangle have to be integers and the hypotenuse is the one that should have the largest value, we can round the value of c up to 115

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The equation of the line is y = 0.5x + 1 having a slope of 0.5 and y intercept of 1

The equation of a line is:

y = mx + b

Where m is the slope and b is the y intercept

From the table shown, the points are:

(-6, -2), (-4, -1), (-2, 0), (0, 1) and (2, 2)

Using any two points to get the equation. Let us use (-2, 0) and (0, 1):

y - 0 = [(1 - 0)/(0-(-2))](x - (-2))

y = 0.5x + 1

The equation of the line is y = 0.5x + 1

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Answer:

A

Step-by-step explanation:

[tex]\sqrt[3]{686x^{4}y^{7}} = \sqrt[3]{343*2x^{3+1}*y^{6+1}}=\sqrt[3]{343*2x^{3}*y^{6}*xy}=\sqrt[3]{7^{3}}\sqrt[3]{x^{3}}\sqrt[3]{y^{6}}\sqrt[3]{2xy}=7xy^{2}\sqrt[3]{2xy}[/tex]

e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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Answer:

x = 10

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{BE}{BF}[/tex] = [tex]\frac{BD}{BC}[/tex] ( substitute values )

[tex]\frac{56+5x-8}{56}[/tex] = [tex]\frac{52+39}{52}[/tex] , that is

[tex]\frac{48+5x}{56}[/tex] = [tex]\frac{91}{52}[/tex] ( cross- multiply )

52(48 + 5x) = 56 × 91 = 5096 ( divide both sides by 52 )

48 + 5x = 98 ( subtract 48 from both sides )

5x = 50 ( divide both sides by 5 )

x = 10

p<4 is the solution of the given inequality.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is -16>-4p

Minus sixteen greater than minus four p

Divide both siders by -4

4>p

p<4

Now we have to draw this on number line.

a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

The attached figure has the graph of p<4.

Hence,  p<4 is the solution of the given inequality.

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Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bottles   Glue   Glitter

1              3.8       1.9

This means,

1 bottle = 3.8 oz of glue and 1.9 oz of glitter

Now,

1 bottle = 3.8 oz of glue

Multiply 4 on both sides.

4 bottle = 4 x 3.8 oz

4 bottle = 15.2 oz

1 bottle = 1.9 oz of glitter

Multiply 4 on both sides.

4 bottle = 7.6 oz

Thus,

15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

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Answer:

47.70

Step-by-step explanation:

6%= 2.7

2.7 +45

=47.7

The number that represents the system in this problem is given as follows:

x = 4.

The number is unknown, hence the variable that represents the number is given as follows:

x.

Then an equality is built from the sentence in the problem, which is then solved to obtain the number.

The addition of 3 to a number is given as follows:

x + 3.

The triple the sum is given as follows:

3(x + 3).

The result is 17 more than the number, hence the equality is given as follows:

3(x + 3) = 17 + x.

Then the solution for the equality, which gives the number, is obtained as follows:

3x + 9 = 17 + x

3x - x = 17 - 9

2x = 8

x = 8/2

x = 4.

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The unit price at Snacks and Healthy are $5.25 and $5.4 respectively.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price, we would determine the unit rate for the cost per pound bag of mixed nut by using the following mathematical expression;

Unit price = Cost of a pound bag of mixed nuts/number of nuts

Substituting the given parameters into the unit price formula, we have the following;

Unit price for Snacks = 15.75/3

Unit price for Snacks = $5.25.

Unit price for Healthy = 13.50/2.5

Unit price for Healthy = $5.4.

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Complete Question:

Snacks and more sells a 3-pound bag of mixed nuts for $15.75. Healthy snacking sells a 2.5-pound bag of mixed nuts for $13.50. What is the unit price at Snacks and Healthy?

Amortization makes up $120.15 of colinda's first monthly mortgage payment.

We must first determine the total amount of Colinda's mortgage in order to determine the amount of her first monthly mortgage payment, which is amortization. Her 20% down payment of $25,000 reduced the mortgage balance to $100,000 ($125,000 – $25,000).

The 30-year term and 5% interest rate on the mortgage result in a $536.82 monthly payment. The portion of the mortgage payment designated for amortization is the sum that is used to pay off the loan's principle; the remainder is used to cover interest.

We can use the following formula to determine the amortization part of the mortgage payment:

Amortization = (Mortgage Payment) - (Interest Payment)

Where:

The mortgage payment ($536.72) is made each month.

Monthly interest payments are computed using the following formula: (Amount of Mortgage) (12%) Interest Rate

When we enter the values, we obtain:

Amortization is calculated as ($536.72) - ($100,000) * (0.05/12)

$536.82 - $416.67 is the amortization.  

Amount amortized : $120.15

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Answer:

[tex]x^2-8x+15=0[/tex]

Step-by-step explanation:

If the roots are [tex]3[/tex] and [tex]5[/tex], the factors are [tex](x-3)[/tex] and [tex](x-5)[/tex].

Taking the leading coefficient as 1, the equation is [tex](x-3)(x-5)=0 \implies x^2-8x+15=0[/tex].

Answer:

Step-by-step explanation: