What is the solution to the equation 4.7x+3.8=13.2?
A.
x=2
B.
x=3
C.
x=3.6
D.
x=3.7

Answer:

60 degrees

Step-by-step explanation:

First of all, we have to set up an equation to solve this. The angles of a triangle add up to 180 degrees. We need to find the internal angle of C, which would be 180-(10x-45).

For our equation, we can set 3x+4x+[180-(10x-45)] equal to 180.

Add like terms:

7x+[180-(10x-45)] = 180

Distribute:

7x+180-10x+45 = 180

Add like terms once again:

-3x+225 = 180

Subtract 225 on both sides:

-3x = -45

Divide by -3 on both sides:

x = 15

Plug in 15 for x in the value 4x:

<B = 60 degrees

This question is incomplete

Complete Question

A varsity boys' basketball team has a ratio of seniors to juniors that is 7:4.

The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors

Answer:

The boys' team has more seniors

Step-by-step explanation:

If each team has 12 juniors,

Step 1

For the boys' basketball team, lets find the total number of people on the team

A varsity boys' basketball team has a ratio of seniors to juniors that is

7:4 = seniors : juniors

Sum of proportion

= 7 + 4 = 11

Let the total number of people on the team = x

Hence:

4/11 × x = 12

4x/11 = 12

Cross Multiply

4x = 11 × 12

x = 11 × 12/4

x = 33 members

The number of seniors is calculated as

33 members - 12 juniors

= 21 seniors

Step 2

For the girls' basketball team, lets find the total number of people on the team

The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2.

= 3:2 = seniors : juniors

Sum of proportion

= 3+2 = 5

Let the total number of people on the team = x

Hence:

2/5 × x = 12

2x/5 = 12

Cross Multiply

2x = 5 × 12

x = 5 × 12/2

x = 30 members

The number of seniors is calculated as

30 members - 12 juniors

= 18 seniors

Therefore, from our above calculations, the boys' team has more seniors

Answer:

x-1+1<15; this gonna be x<15 and 1x-1+1>15 this is gonna be the same

Step-by-step explanation:

a) The central 95% of all copper contents would be bounded by the values of 26.02 and 35.58.

b) The distribution of the sample mean copper content follows an approximately normal distribution with a mean of 30.8 and a standard error of \($\frac{2.45}{\sqrt{16}}\) =0.6125.

c) If we were to randomly sample 16 brake pads from this distribution, the bounding values for the central 95% of possible means would be (29.6, 32)

a) Since the copper content in sintered brake pads follows an approximately normal distribution with a mean of 30.8 and a standard deviation of 2.45, we can use the standard normal distribution to find the values that bound the central 95% of all copper contents. The 95% confidence interval corresponds to z=1.96 in the standard normal distribution. Thus, the values that bound the central 95% of all copper contents are given by:

30.8−1.96×2.45=26.02,30.8+1.96×2.45=35.58

b) The sample mean of copper content for a sample of 16 pads is also normally distributed with a mean of 30.8 and a standard deviation of \($\frac{2.45}{\sqrt{16}}=0.6125$\), which is called the standard error. The distribution of the sample mean is given by:

c) The bounding values for the central 95% of possible means can be found by using the formula:

where \($\sigma$\) is the population standard deviation, n is the sample size and \($z^*$\)is the critical value of the standard normal distribution that corresponds to a 95% confidence interval. Substituting the values, we get:

Therefore, the bounding values for the central 95% of possible means are given by:

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Answer:

$0.696 or $0.70

Step-by-step explanation:

0.90+0.42+0.78+0.13+1.25= 3.48

3.48 ÷ 5 =0.696

(You divide by five because there are five sets of number)

Answer:

$0.90 + $0.42 + $0.78 + $0.13 + $1.25 divid by 5 =

= 0.696

Step-by-step explanation:

Answer = 0.696

Answer:

D.

Step-by-step explanation:

By looking at them I feel like D. is the best option

The area under the standard normal curve where P(-0.88 < Z < 0) is 0.3106. The area under the standard normal curve where P(Z > 0.77) is 0.2207. Option (1)

In probability theory, the standard normal distribution is a normal distribution of a random variable with mean 0 and standard deviation 1. The area under the standard normal curve can be calculated using tables or software.

For the first question, we are given P(-0.88 < Z < 0) and we need to find the area under the standard normal curve that corresponds to this probability. Using a standard normal distribution table, we can look up the values of -0.88 and 0 and find the corresponding areas, then subtract the smaller area from the larger area to get the answer. The correct answer is 0.3106.

For the second question, we need to find the area under the standard normal curve that corresponds to P(Z > 0.77). Since the standard normal distribution is symmetric, we can find the area to the left of 0.77 and subtract it from 1 to get the answer.

Again, using a standard normal distribution table, we can look up the value of 0.77 and find the corresponding area, then subtract it from 1. The correct answer is 0.2207.

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Full Question : The area under the standard normal curve where P(-0.88 < Z < 0) is: O 0.1894 0.2709 ○ 0.3106 O0.8106 06894 D Question 2 : The area under the standard normal curve where P(Z > 0.77) is:

Answer:

2nd option is the right answer

Answer:

yes

Step-by-step explanation:

there are variables so it is a function

Answer:

Yes, x^2 + 2y = 4 is a function.

Step-by-step explanation:

x^2 + 2y = 4

Solve for y.

2y = -x^2 + 4

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

f(x) = -(1/2)x^2 + 2

Answer: Yes, x^2 + 2y = 4 is a function.

Answer:

f(x) = -x -11

    = -9-11 = -20

f(x) = -x-11

    = -6-11= -17

Step-by-step explanation:

Answer:

It is already the farthest that can be

Step-by-step explanation:

5x4 - 7x3 + x + 2

5x^2 - 7x^2 + 1x + 2

Answer:

create common denominator

Step-by-step explanation:

1/4 can become 2/8 by multiplying the top and bottom number by 2 now you have a common denominator to add 2/8+3/8 = 5/8

Thus, it will take 2 years 8 months for Gabriella to save up $4,800 for the air conditioner.

We have to determine the variable separately or isolate the variable across one side when evaluating an equation for a variable.

A linear equation is one in which the maximum possible power of both the variables is 1. In other words, a linear equation as in variable "x" is one that has the form of axe + b = c, where a, b, and c are constants, a 0, and "x" is the variable.

In the given question:

Total price of air conditioner including tax = $4,800.

Savings per month =  $150

Let 'n' be the number of months.

Then, one variable linear equation forms:

150n = 4800

n = 4800 / 150

n = 320 months

n = 2 years 8 months

Thus, it will take 2 years 8 months for Gabriella to save up $4,800 for the air conditioner.

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Answer:

9

Step-by-step explanation:

Since each driver can cover at most one route, we will continuous this process until all 12 routes have been assigned to a driver. This will ensure that the school system pays the least amount possible for the 12 bus routes.

To minimize the school system's cost while assigning drivers to the bus routes, follow these steps:

1. Open the file P05_45.xlsx and arrange the data in a clear format, such as a table with drivers listed vertically and routes listed horizontally. Each cell should contain the amount a driver charges for a specific route.

2. Identify the lowest bid for each route. You can do this by going through each column (representing a route) and finding the minimum amount.

3. Assign the driver with the lowest bid to the corresponding route. Make sure to keep track of which drivers have already been assigned to avoid assigning them to multiple routes.

4. Continue this process for all 12 routes. Remember, each of the 16 drivers can only be assigned to one route.

5. Once all drivers have been assigned to the routes, add up the amounts for each assigned driver to find the total cost for the school system.

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Triangle DEF is congruent to triangle SRU, i.e., ΔDEF ≅ ΔSRU. So, second option is correct.

It is given to us that -

Triangle DEF is reflected over the y-axis

It is then translated down 4 units and right 3 units

We have to find out the correct congruency statement that describes the figures.

From the given figures we can see that, upon translation of the triangle DEF down 4 units and right 3 units,

The point D gets transformed into S

The point E gets transformed into R

The point F gets transformed into U

We know that any type of rotation or translation does not create any change in the shapes or dimensions of the figure.

So, the lengths and angles didn't vary in accordance to the given transformations.

Therefore, the new triangle is ultimately congruent to the actual triangle.

Thus, corresponding to the equivalent order for the letters of the original triangle, it can be concluded that triangle DEF is congruent to triangle SRU, i.e., ΔDEF ≅ ΔSRU. So, second option is correct.

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The equation in rectangular coordinates for the surface represented by the cylindrical equation r = 4 sin(θ) is x² + y² = 4y. The equation in rectangular coordinates for the surface represented by the cylindrical equation r = 7 cos(θ) is x² + y² = 7x.

To convert a cylindrical equation to rectangular coordinates, we can use the following conversions: r = \(\sqrt{(x^2 + y^2)}\) and θ = tan⁻¹(y/x).

For the cylindrical equation r = 4 sin(θ):

Substituting the conversion formulas, we have:

\(\sqrt{(x^2 + y^2)}\) = 4 sin(θ)

Squaring both sides of the equation, we get:

x² + y² = 16 sin²(θ)

Using the identity sin²(θ) = 1 - cos²(θ), we have:

x² + y² = 16(1 - cos²(θ))

Since cos²(θ) = 1 - sin²(θ), the equation becomes:

x² + y² = 16(1 - sin²(θ))

Simplifying further, we have:

x² + y² = 16 - 16sin²(θ)

Using the trigonometric identity sin²(θ) = (1/2)(1 - cos(2θ)), the equation becomes:

x² + y² = 16 - 8(1 - cos(2θ))

Finally, substituting cos(2θ) = 2cos²(θ) - 1, we have:

x² + y² = 8 + 8cos(2θ)

For the cylindrical equation r = 7 cos(θ):

Following the same steps as above, we substitute the conversion formulas and simplify to obtain:

x² + y² = 49 cos(2θ)

Therefore, the equation in rectangular coordinates for the surface represented by the cylindrical equation

r = 4 sin(θ) is x² + y² = 8 + 8cos(2θ),

and the equation in rectangular coordinates for the surface represented by the cylindrical equation r = 7 cos(θ) is x² + y² = 49 cos(2θ).

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The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.

It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.

According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.

Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;

8/10 = 3/x

x = ( 10 × 3 ) / 8

x = 30/8

x = 3.75 inches.

Therefore, the width on the scale as required is; 3.75 inches.

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A dealer bought some 9-volt batteries for $2,400. She sold them for $5,600, making a profit of $1.60 on each battery. 2,500 batteries were involved in the deal.

The dealer bought some 9-volt batteries for $2,400 and she sold them for $5,600. To find out how many batteries were involved, we need to calculate how much she made from each battery. We can do this by subtracting the cost of the batteries from the selling price and then dividing it by the number of batteries. Profit per battery = $5,600 - $2,400 = $3,200. Number of batteries = $3,200/$1.60 = 2,500. Therefore, the dealer bought 2,500 batteries.

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The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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180° rotation rule  (x, y) → (–x, –y)..

Triangle XYZ is rotated to create the image triangle X'Y'Z'. On a coordinate plane, 2 triangles are shown.

The first triangle has points X (-5, 3), Y (-2, 3), Z (2, 1).

The second triangle has points X prime (5, - 1), Y prime (5, - 4), Z prime

(3, - 4).

Here the sign of both coordinates has been changed but the magnitude remains same.

So, the rule is  (x, y) → (–x, –y)  which is for 180° rotation.

Hence, the  180° rotation rule  (x, y) → (–x, –y).

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20 m longer  to walk from A to B along the diagonal of the park than to walk along the edges of the park.

What is rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. It can alternatively be described as a parallelogram with a right angle, an equiangular quadrilateral, or a group of triangles with equal angles. A square is a rectangle that has four equal sides.

As given, a park is in the shape of a rectangle and measures length of

40 m and width of 30 m, ∠B = 90°.

So, by Pythagoras theorem,

\(AC^2 = AB^2 + BC^2\\AC^2 = (40)^2 + (30)^2\\AC^2 = 1600 + 900\\AC^2 = 2500\\AC = \sqrt{2500}\\ AC = 50\)

So, the distance from A to B along the diagonal is,

AB = AC + BC = 50 + 40 = 90 m

The distance from A to B along with the edges is,

AB = AD + DC + CB = 40 + 30 + 40 = 110 m.

Therefore, 20 m longer  to walk from A to B along the diagonal of the park than to walk along the edges of the park.

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The order of the differential equation d²y/dx² + 4x(dy/dx) = d³(cos(2x))/dx³ is 3.

The order of a differential equation is determined by the highest derivative present in the equation. In the given differential equation, the highest derivative is the third derivative, d³(cos(2x))/dx³. Since this is the highest derivative and there are no higher-order derivatives present, the order of the differential equation is 3. This means that the equation involves up to the third derivative of the dependent variable y with respect to the independent variable x.

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The probability that exactly six out of the eight babies are girls is approximately 0.109375, or 10.9375%.

To calculate the probability that exactly six of the eight babies are girls, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k successes (in this case, girls)

C(n, k) is the number of combinations (ways) to choose k successes from n trials

p is the probability of success in a single trial (in this case, the probability of having a girl)

n is the total number of trials (in this case, the number of babies)

In this scenario, we want to find the probability that exactly six out of the eight babies are girls. Assuming each baby has an equal chance of being a boy or a girl, the probability of having a girl is 0.5 (or 1/2).

Using the binomial probability formula, we can calculate:

P(X = 6) = C(8, 6) * (0.5)^6 * (1 - 0.5)^(8 - 6)

C(8, 6) represents the number of ways to choose 6 girls out of 8 babies, which is given by the binomial coefficient:

C(8, 6) = 8! / (6! * (8-6)!)

= 8! / (6! * 2!)

= (8 * 7) / (2 * 1)

= 28

Substituting the values into the formula:

P(X = 6) = 28 * (0.5)^6 * (0.5)^2

= 28 * (0.5)^8

= 0.109375

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The constant term of the polynomial \(2x^3 - 8x^2+ 3x -7\\\) is -7

What is a polynomial?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division sign.

A mathematical expression of the form \(a_0 + a_1x + a_2x^2 + .... + a_nx^n, (a_n \neq 0)\) is called a polynomial of degree n

Here the polynomial is

\(2x^3 - 8x^2+ 3x -7\\\)

There is no variable associated with the term -7

So the constant in this polynomial is -7

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Correct Question

What is the constant of this polynomial?

\(2x^3 - 8x^2+ 3x -7\\\)

Answer:

I think the answer to it is B