Solve x+x+x=54

Solve y\5=7

Solve 4t+6=24

Answer:

£1200

Step-by-step explanation:

25% reduction represents 75% of the original price of 100%

Divide the cost by 75 to find 1% and multiply by 100

\(\frac{900}{75}\) × 100 = 12 × 100 = £1200

Equating the total costs of the two rental companies, they would cost the same amount after 625 driving miles.

An equation is a mathematical statement that claims that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to depict the equality of the expressions.

                                  Company A    Company B

Fixed rental charge         $75                 $100

Rental charge per mile  $0.07              $0.03

Let the number of miles driven = m

Total cost of Company A's rental = 75 + 0.07m

Total cost of Company B's rental = 100 + 0.03m

For the cost to be the same, 75 + 0.07m = 100 + 0.03m.

Solving for m:

75 + 0.07m = 100 + 0.03m

0.07m - 0.03m = 100 - 75

0.04m = 25

m = 625

Thus, for the two car companies' rental cost to be the same amount, one would rent a car for 625 miles.

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Answer:

Let the adjacent angles of the rhombus be 2x and 3x. We know that the sum of the measures of the adjacent angles is equal to 180°. AD = DC = 3 × 36° = 108°. Hence , the angles of the rhombus are 72° , 108° , 72° and 108°.

Step-by-step explanation:

Answer:

Let the adjacent angles of the rhombus be 2x and 3x.

we know that the sum of the measures of the adjacent angles is equal to 180°.

2x+3x=180

=5x=180

=x=180/5

=x=36°

Hence,AB =BC=2×36°=72°

AD=DC=3×36°=108°

Hence,The angles of the rhombus are 72°,108°, 72°and108°.

I hope it's helpful!

The distribution of X is (6,11).

Suppose the time it takes your daughter Lizzie to eat an apple is uniformly distributed between 6 and 11 minutes.

Let X represent the time it takes Lizzie to eat an apple.

The distribution of X can be described as follows,

X ~ Uniform(6, 11) which means the time it takes Lizzie to eat an apple, represented by the random variable X, follows a uniform distribution with a minimum value of 6 minutes and a maximum value of 11 minutes. In this distribution, every time interval between 6 and 11 minutes has an equal probability of occurring.

The distribution of X which represents the time it takes Lizzie to eat an apple is uniformly distributed between 6 and 11 minutes.

Therefore, we can write X ~ Uniform(6,11).

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The alternative hypothesis that will give the smallest P-value is a. μd ​≠ 0.

This is because the alternative hypothesis μd ​≠ 0 is a two-tailed test, meaning that it considers both the possibility of μd being less than 0 and greater than 0.

This means that there are two areas in the tail of the distribution that are considered when calculating the P-value, leading to a smaller P-value.The other two alternative hypotheses, μd ​< 0 and μd ​> 0, are one-tailed tests and only consider one area in the tail of the distribution, leading to larger P-values.

Therefore, the alternative hypothesis μd ​≠ 0 will give the smallest P-value.

A p-value is a statistical measurement used to validate a hypothesis against observed data. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. The lower the p-value, the greater the statistical significance of the observed difference.

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Using recursive formula, 5 is the next term in sequence.

The given recursive formula for the sequence is f(n + 1) = f(n) + 3, where f(n) represents the nth term of the sequence.

Given that the first term of the sequence is -4, we can use the recursive formula to find the next term:

Starting with the first term of -4, we apply the recursive formula to find subsequent terms. The formula states that each term is obtained by adding 3 to the previous term.

So, for the second term, we add 3 to the first term: -4 + 3 = -1.

For the third term, we add 3 to the second term: -1 + 3 = 2.

And for the fourth term, we add 3 to the third term: 2 + 3 = 5.

Hence, the next term in the sequence is 5.

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The probability illustrated here is experimental. So the correct option is Option A

When we roll a dice which have a number 1 to 6, once. Then the probability of obtaining each number becomes

                                       P=1/6                                          

                                       =0.17

Now, when we roll a dice 12 times, the probability of obtaining each number becomes

                                    P = [1/6]¹²

As we can see here it is given that,

                                      P(5) = 2/3

                                              = 0.67

Which shows it is experimental probability rather than theoretical probability

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Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

42b -7.5

I think that's the answer since you are getting a discount which means you are subtracting

The area of each of the missing faces is 40 m².

The length of each of the missing faces is 10 m.

The missing dimension is 10 m by 4 m.

Area is the region bounded by a plane shape.

To calculate the area of each missing face, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

And the length of each of the missing edge can be calculated using the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute into equation 2

Hence, the length is 10 m.

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Answer:

8/37

Step-by-step explanation:

People who wants iced tea = 45 - 8

People who wants lemonade = 8

8 (lemonade) / 37 (iced tea)

Type fish A are 8 inches long and Type B fish are 7 inches long.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Marta's aquarium holds 38 gallons of water

and Hank's aquarium hold 52 gallons of water.

let length of fish A be x

and, the length of type B be y.

So, 3x+ 2y = 38

and, 3x+ 4y = 52

Solving above equation

2y = 52-38

2y = 14

y=7

and, 3x+ 2(7) = 38

3x = 38-14

3x= 24

x= 24/3

x= 8

Hence, Type fish A are 8 inches long and Type B fish are 7 inches long.

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Answer:

llllllllllsgduehidhejeiwhu

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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The given equation 3x^2 - y^2 + z^2 = 0 represents a surface known as an elliptic paraboloid. To sketch this surface using traces, we can fix one variable (either x, y, or z) and vary the other two to observe the resulting curve.

Let's fix x at a constant value of 0. Substituting x = 0 into the equation, we get -y^2 + z^2 = 0. This equation represents a pair of intersecting lines, forming a trace. By varying x and fixing y or z, we can obtain additional traces, which are also pairs of intersecting lines.

Thus, by considering multiple traces, we can sketch the elliptic paraboloid surface, which resembles a bowl or a saddle. The traces consist of intersecting lines that form a grid-like pattern on the surface.

Now, moving on to the second question, we are given two skew lines with parametric equations. To find the distance between these lines, we can use the closest distance formula.

First, we need to find a point on each line. By setting t = 0 in the first line's equations, we find a point (2, 3, 0). Similarly, setting s = 0 in the second line's equations gives us a point (1, 6, -2).

Next, we find the direction vectors for both lines. The direction vector for the first line is <1, 6, 2>, and for the second line is <2, 14, 5>.

Using the closest distance formula, we can calculate the distance between the two lines as follows:

distance = |(2-1, 3-6, 0+2) · (1, 6, 2) x (2, 14, 5)| / |(1, 6, 2) x (2, 14, 5)|

Simplifying this expression will give us the distance between the skew lines.

Please note that the exact calculations are omitted here, but following the steps outlined above will provide the desired distance.

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Answer:

A and C is true statements

Answer:

$159.25 is what she had the last month because

Step-by-step explanation:

91/100x75/1=6825 simplified and you get 159.25

The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the quadrilateral be represented as ABCD

Now , the coordinates of ABCD is given as

A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )

Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin

Substituting the values in the equation , we get

A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )

On simplifying the equation , we get

The coordinates of A' is = A' ( -2 , 4 )

The coordinates of B' is = B' ( 4 , 4 )

The coordinates of C' is = C' ( 6 , -2 )

The coordinates of D' is = D' ( 0 , -2 )

Hence , the dilated figure is solved

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Step-by-step explanation:

2057 smartphone users bought something after searching for information. The standard error of the proportion (SE) measures variability in the estimated proportion and assesses estimate precision. The standard error of a proportion formula can be used to compute SE. 4024 smartphone users participated in this poll.

The count X is the number of smartphone users who reported purchasing an item after using their smartphones to search for information about it. In this case, X is given as 2057.

To calculate the standard error of the proportion (SE), we need to know the sample size (n) and the proportion (p) of smartphone users who made a purchase after searching for information. The formula for SE of a proportion is:

SE = sqrt((p * (1 - p)) / n)

Since the proportion is not given directly, we can estimate it by dividing X (the count) by the sample size (n):

p = X / n

Substituting the values, we can calculate SE:

SE = sqrt((2057/4024) * (1 - 2057/4024) / 4024)

After performing the calculations, we find that the standard error (SE) is a decimal value. To report it accurately, we round it to three decimal places.

The sample size (n) for this survey is provided in the question as 4024. This represents the total number of smartphone users who participated in the study and responded to the questions.

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The number of bananas required to make the third scale balance is 3.

A scale is a tool used for weighting objects. If the objects on each side weigh the same the scale is balanced. Based on this, let's determine the possible weight of each fruit to balance the last scale.

It is known 10 bananas weigh as much as 2 apples, but to solve this problem let's assume 10 bananas weigh a total of 1000 grams.

Scale 2 ( 1 pineapple / 2 bananas, 1 apple)

Using the same imaginary weights let's find the weight of the apple.

Scale 3 (1 apple /x )

We know 1 apple is equal to 300 grams and 1 banana is equal to 100 grams. Based on this, the number of bananas to balance the scale is 3.

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The percentage error for the circumference ≈ -95.53% and the percentage error for the area ≈ -98.23%

Provided:

Exact diameter = 188 cm

Measured diameter = 8.2 cm

To calculate the percentage error in the circumference of a circle, we'll use the formula:

\(\[\text{{Percentage Error in Circumference}} = \left( \frac{{\text{{Measured Circumference}} - \text{{Exact Circumference}}}}{{\text{{Exact Circumference}}}} \right) \times 100\]\)

Exact Circumference = π * Exact Diameter = π * 188 cm

Measured Circumference = π * Measured Diameter = π * 8.2 cm

\(\[\text{Percentage Error in Circumference} = \left(\frac{\pi \cdot 8.2 \, \text{cm} - \pi \cdot 188 \, \text{cm}}{\pi \cdot 188 \, \text{cm}}\right) \times 100\]\)

\(\[=\frac{{8.2 \, \text{cm} - 188 \, \text{cm}}}{{188 \, \text{cm}}} \times 100 \\\\= \frac{{-179.8 \, \text{cm}}}{{188 \, \text{cm}}} \times 100\]\)

≈ -95.53%

Next, to calculate the percentage error in the area of a circle, we'll use the formula:

Percentage Error in Area = \(\(\left(\frac{{\text{{Measured Area}} - \text{{Exact Area}}}}{{\text{{Exact Area}}}}\right) \times 100\)\)

Exact Area = π * (Exact Radius)²

Exact Radius = \(\frac{Exact Diameter}{2}\)

Substituting the values:

Exact Radius = \(\frac{ 188 cm}{2}\)

Measured Radius = \(\frac{8.2 cm}{2}\)

Measured Area = π * (Measured Radius)²

Measured Radius = \(\frac{Measured Diameter}{2}\)

Substituting the values:

Exact Area = π * \((\frac{188 cm}{2} )^2\)

Measured Area = π * \((\frac{8.2 cm}{2} )^2\)

∴ Percentage Error in Area \(=$\left(\frac{\pi \left(\frac{8.2 \text{ cm}}{2}\right)^2 - \pi \left(\frac{188 \text{ cm}}{2}\right)^2}{\pi \left(\frac{188 \text{ cm}}{2}\right)^2}\right) \times 100$\)

\(= \[\frac{{\left(\frac{{8.2 \, \text{cm}}}{2}\right)^2 - \left(\frac{{188 \, \text{cm}}}{2}\right)^2}}{{\left(\frac{{188 \, \text{cm}}}{2}\right)^2}} \times 100\]\)

\(= \[\frac{{(2.05 \, \text{cm})^2 - (47 \, \text{cm})^2}}{{(47 \, \text{cm})^2}} \times 100\]\)

≈ -98.23%

Therefore, the calculated percentage errors are approximately -95.53% for the circumference and -98.23% for the area.

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Answer: 6 fertilizer

Step-by-step explanation:

Take 120 divided by 4 = 30 soil per fertilizer

We know that 30 times 6 = 180

So we take 1 time 6 =  6 Fertilizer

Answer:

Step-by-step explanation:

you can solve with a simple proportion

4 : 120 = x : 180

x = 4 x 180 : 120

x = 6

Answer:

56

Step-by-step explanation:

56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34

Answer:

Asymptotes can be defined as lines that the curve approaches but never touches or crosses.

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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If rxy = 0.83, we can conclude that x and y have a relatively strong positive linear relationship or correlation.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, in this case, x and y. The value of r ranges between -1 and 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable tends to increase as well.

In this case, with rxy = 0.83, the correlation coefficient is close to 1, suggesting a strong positive linear relationship. This means that when x increases, y also tends to increase, and vice versa. The closer the value of r is to 1, the stronger the linear relationship between x and y.

It is important to note that correlation does not imply causation. While a high correlation coefficient indicates a strong linear relationship, it does not provide information about the underlying cause or direction of the relationship between the variables. Other factors and variables may influence the relationship, and further analysis may be required to understand the nature of the relationship between x and y.

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The mean of the Poisson distribution is given as follows:

\(\mu = 4\)

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

The probability of at most 1 is given as follows:

P(X≤1) = P(X = 0) + P(X = 1).

From the conditional probability, we have that:

P(X = 1)/[P(X = 0) + P(X = 1)] = 0.8

P(X = 1) = 0.8P(X = 0) + 0.8P(X = 1)

0.2P(X = 1) = 0.8P(X = 0)

P(X = 1) = 4P(X = 0).

Hence the mean is obtained as follows:

\(\mue^{-\mu} = 4e^{-\mu}\)

\(\mu = 4\)

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We can match each of the following events with the best description of their probability as follows:

Landing on a number greater than 6 = as likely as not

Landing on the number 0 = unlikely

Landing on an odd number = likely

Landing on a number greater than 2 = Certain

To determine the probabilities, we could first assign the entire numbers to be obtained as 8. Next, we use the statements given to determine the likely probabilities. For instance, the likelihood of getting a number greater than 6 gives us the numbers, 7 and 8.

Now, we sum these up and obtain the probability. This gives us 2/8 which is equal to 0.25. So, it is possible to get a number greater than 6 when the spinner is spun.

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