The ratio of the present age of mother and daughter is 3:1. Six years ago the ratio of their age was 6 : 1. Find their present age.​

the probability that she picks 2 different types of drink is 71 / 105

let say E is an event then ,P(E) = favourable outcome /total outcome

given that ,

3 bottles of orange juice.

5 bottles of apple juice.

7 bottles of water.

Then  total of 3 + 5 + 7 = 15 bottles of drinks .

To calculate the probability of picking 2 different types of drinks, we need to calculate the total number of possible pairs of drinks that can be picked, and the number of pairs that consist of different types of drinks.

so,

The total number of possible pairs of drinks that can be picked is given by the combination formula:

C(15, 2) = 15! / (2! * (15-2)!) = 105

This formula calculates the number of ways to choose 2 items from a set of 15 items.

Now, the number of pairs that consist of different types of drinks. There are three types of pairs : orange juice and apple juice, orange juice and water, and apple juice and water.

The number of pairs of different types of drinks :

(3 * 5) + (3 * 7) + (5 * 7) = 15 + 21 + 35 = 71

So, the probability of picking 2 different types of drinks is:

71 / 105 ≈ 0.6762 or about 67.62%.

more about probability visit:

https://brainly.com/question/30034780

#SPJ1

Answer:

1. first option

2. second option

3. second option

Step-by-step explanation:

i dunno i did the math and used a calculator. im pretty confident with my answers so hopefully theyre right

The null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

Null hypothesis is a statistical hypothesis that claims there is no significant difference between a specified population parameter and the observed sample statistics. While alternative hypothesis is a statistical hypothesis that suggests that there is a significant difference between a specified population parameter and the observed sample statistics.In the given scenario, the null hypothesis and the alternative hypothesis will be:

Null hypothesis (H0): At most 70% of people who eat fast food more than 2x a week are overweight. (This means less than 70% are overweight)Alternative hypothesis (Ha): More than 70% of people who eat fast food more than 2x a week are overweight.

:We can evaluate the null hypothesis by testing the probability of a sample occurring, assuming the null hypothesis is true. If the probability of a sample is very low, it implies that it is unlikely that the sample was obtained assuming that the null hypothesis was true, and we can reject the null hypothesis and accept the alternative hypothesis

.In conclusion, the null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

To know more about null hypothesis visit:

brainly.com/question/30821298

#SPJ11

Answer:

x=2

Step-by-step explanation:

You have to subtract 8 from both sides.

-5x+8=-2

-8 -8

----------------

-5x= -10

now divide both sides by -5.

x=-10/-5

(And two negatives make a positive.)

x=10/5

now you have to simplify 10/5

10/5 simplified is 2

so the answer is:

x=2

I hope this helps. :)

n = 37, and tenth term = 18

Given progression,

36, 34, 32, ...

The sum of the first n terms is 0

First term(a1) = 36

The common difference (d)= 34-36 = -2,

The formula of the sum of the first n term is,

\(Sn = \frac{n}{2} [2a_{1} + (n - 1)d]\)

substitue the values Sn= 0, a1= 36, d= -2 in the above equation to find n

\(0\)= \(\frac{n}{2} [2(36) + (n-1) (-2)]\)

\(0 = \frac{n}{2}[72- 2n+ 2]\)

\(0 = \frac{n}{2}[74 - 2n]\)

\(74 - 2n = 0\)

\(2n = 74\)

\(n = \frac{74}{2}\)

\(n = 37\)

n = 37

The formula for finding the nth term(10th term):

\(a_{n} = a1 + (n - 1)d\)

n = 10, a1 = 36, d = -2

\(a_{10} = 36 + (10-1)(-2)\)

\(a_{10} = 36 + 9(-2)\)

\(a_{10} = 36 - 18\)

\(a_{10} = 18\)

\(a_{10}\) = 18

To solve more problems on progression:

https://brainly.com/question/6561461

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

Learn more about probability, here:

https://brainly.com/question/30034780

#SPJ1

The fraction of the 30 cakes does Simon have left with os 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, Simon makes 30 cakes, he gives 1/5 of the cakes to Sali, he gives 10% of the 30 cakes to Jane,

We need to find, what fraction of the 30 cakes does Simon have left,

Number of cakes given to Sali = 1/5 of 30

= 30 / 5 = 6

That mean, Sali got 6 cakes out of 30.

Number of cakes given to Jane = 10% of 30

= 30 × 10/100

= 300 / 100

= 3

That mean, Jane got 3 cakes, out of 30.

The remaining number of cake = 30 - (6+3)

= 30 - 9

= 21

Therefore, the fraction of cakes left = 21 / 30

= 7/10

Hence, the fraction of the 30 cakes does Simon have left with os 7/10

Learn more about fractions, click;

https://brainly.com/question/1301963

#SPJ1

Answer: B

Step-by-step explanation: I'm sorry if I'm wrong

Answer:

Composition and vertical translation must be done in the parent function.

Step-by-step explanation:

Let be \(j(x)\) the parent function, if \(g(x) = j(4\cdot x) -27\), then two transformation must be done in the following order:

Composition

\(j \circ h (x) \rightarrow j(h(x))\), where \(h(x) = 4\cdot x\)

Vertical translation

\(g(x) = j(4\cdot x) -27\)

Composition and vertical translation must be done in the parent function.

Answer: Option D

Horizontal compression by a factor of 1/4, and a translation 27 units down

Answer:

\(y=-\frac{2}{3}x+1\)

Step-by-step explanation:

Parallel means same slope.

\(y=-\frac{2}{3}x+b\)

\(5=-\frac{2}{3} (-6)+b\)

5 = 4 + b

b = 1

\(y=-\frac{2}{3}x+1\)

Answer: x = 35/13

Step-by-step explanation:

Answer:

11.7

Step-by-step explanation:

1111111938338388383828

Answer:

157.62

Step-by-step explanation:

I took the mass(g) of 34.932 and divided it by the volume of 4.1

\(\frac{34.932}{4.1} =8.52\)

To prove that this was correct I did the same thing for the next row

\(\frac{47.712}{5.6} =8.52\)

I took 8.52 and multiplied it by the volume of 18.5 to get the mass.

\(8.52*18.5=157.62\)

The mass is 157.62

hope this helps! :))

By running the script or calling the function with different values of x, y, and R, you can simulate the behavior of the given function and determine its output based on the conditions specified.

Here's a MATLAB code snippet that simulates the function M(x, y):

function result = M(x, y, R)

   if x^2 + y^2 <= R^2

       result = 1;

   else

       result = 0;

   end

end

To use this function, you can call it with the values of x, y, and R and it will return the corresponding result based on the conditions specified in the function.

For example, let's say you want to evaluate M for x = 3, y = 4, and R = 5. You can do the following:

x = 3;

y = 4;

R = 5;

result = M(x, y, R);

disp(result);

The output will be 1 since x^2 + y^2 = 3^2 + 4^2 = 25, which is less than or equal to R^2 = 5^2 = 25.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

The mean and variance of the area A of a circle with a random radius R, uniformly distributed between 0 and 1, can be calculated using mathematical formulas. The mean of A is π/4, and the variance of A is (π^2 - 4)/16.

The area A of a circle is given by the formula A = π * R^2, where R is the radius. Since the radius R is uniformly distributed between 0 and 1, we can express the probability density function (PDF) of R as f(R) = 1 for 0 ≤ R ≤ 1, and f(R) = 0 elsewhere.

To find the mean of A, we need to calculate the expected value of A, denoted as E[A]. Using the formula for expected value, we have E[A] = ∫(A * f(R)) dR = ∫(π * R^2) dR from 0 to 1. Solving this integral gives E[A] = π/4.

To find the variance of A, we need to calculate E[A^2] first. Using the formula for expected value, we have E[A^2] = ∫(A^2 * f(R)) dR = ∫(π^2 * R^4) dR from 0 to 1. Solving this integral gives E[A^2] = π^2/5.

The variance of A can be calculated as Var[A] = E[A^2] - (E[A])^2 = π^2/5 - (π/4)^2 = (π^2 - 4)/16.

Therefore, the mean of A is π/4, and the variance of A is (π^2 - 4)/16 for a circle with a random radius R uniformly distributed between 0 and 1.

Learn more about circle here:

https://brainly.com/question/12930236

#SPJ11

Answer:

y = 6x - 14

General Formulas and Concepts:

Pre-Algebra

Algebra I

Equality Properties

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

[Point-Slope Form]   y - 4 = 6(x - 3)

Step 2: Rewrite

Find Slope-Intercept Form.

Answer: A.

Step-by-step explanation:

yeet

Answer:

A.

Step-by-step explanation:

Because if you multiply out the top of the fraction to simplify it, it will equal zero. And zero divided by any number is equal to zero because no number fits into zero. So A. would be the best answer since you are multiplying an expression by zero on the top, and you can't get any number other then zero for the answer of the fraction. And 0 + 9.4 = 9.4.

Here, we want to describe the difference between relative frequency and theoretical probability

Firstly, we need the values for the theoretical probability and relative frequency

To get the theoretical probability, we only need to divide the number of frequencies of lizards by the total frequency

The total frequency is;

13 + 7 + 5 + 10 + 7 + 5 = 47

The theoretical probability is thus;

Now, we need the value for the relative frequency

That would be expressed as a percentage and that is;

Answer:

The equation of a line in the slope-intercept form is:

y = 5x - 18

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where

In our case, we are given

now substituting m = 5 and (4, 2) in the slope-intercept form of the line equation to determine the y-intercept

y = mx + b

2 = 5(4) + b

20 + b = 2

subtract 20 from both side

20 + b - 20 = 2 - 20

b = -18

now substituting b = -18 and m = 5 in the slope-intercept form of the line equation

y = mx + b

y = 5x + (-18)

y = 5x - 18

Therefore, the equation of a line in the slope-intercept form is:

y = 5x - 18

To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

Learn more about Cubic Formula here :

https://brainly.com/question/27377982

#SPJ11

\( \sf \: I = P(1 + \frac{r}{n} {)}^{nt} - P \\ \sf = 893(1 + \frac{41}{500} ) ^{1 \times 5} - 893 \\ \sf= 893 \times ( \frac{541}{500} ) ^{5} - 893 \\ \sf= 1324.30 - 893 \\ \sf = 431.30\)

Answer:

$431.30(approximate value)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

B. y = -5/4x + 3

Step-by-step explanation:

The slope is negative because the line is going from up to down.

Options A and C are wrong.

To find the slope divide by difference of two points.

(0, 3) and (4, -2)

(-2-3)/(4-0)

-5/4

The slope is -5/4.

The y-intercept is (0, 3)

y = mx + b, m is the slope and b is the y-intercept.

y = -5/4x + 3

The length of the shorter leg of the triangle ABC is approximately 24.49 units. Let's denote the right triangle ABC, where C is the right angle.

Let D be the midpoint of AB, and E be the foot of the altitude from C to AB. Then we have:

CD = 1/2 AB (definition of median)

CE = 12 (given altitude to the hypotenuse)

Let x be the length of the shorter leg of the triangle ABC. Then we have:

AE = x (definition of altitude)

EB = AB - x (definition of complementary leg)

By the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

(2CD)^2 = AB^2 + x^2

AB^2 = 4CD^2 - x^2

By the similarity of triangles AEC and ABC, we have:

CE/AC = AE/AB

12 / (AB + BC) = x / AB

AB = x / (12/x + 1)

Substituting AB into the previous equation, we get:

4CD^2 - x^2 = x^2 / (12/x + 1)^2

Simplifying and solving for x, we get:

x^4 - 576x^2 - 14400 = 0

This is a quadratic equation in x^2, so we can solve for it using the quadratic formula:

x^2 = [576 ± sqrt(576^2 + 4*14400)] / 2

x^2 = [576 ± 624] / 2

Since x is a length, we take the positive square root:

x^2 = 600

x ≈ 24.49

Therefore, the length of the shorter leg of the triangle ABC is approximately 24.49 units.

Learn more about triangle here:

https://brainly.com/question/2773823

#SPJ11

The present value of the payments is smaller than the amount of the loan, so you will not be able to pay off the loan.

The present value of the payments refers to the current value of the future payments, considering the time value of money. In this case, the payments are made over a period of 8 months, and each payment is listed. To determine if the payments will be enough to pay off the credit card, we need to calculate the present value of these payments and compare it to the initial loan amount of $5,000.

Since the interest rate on the credit card is 1.5% per month, we need to discount each payment back to its present value. By discounting the payments, we can see the equivalent value of these payments in today's dollars. If the present value of the payments is equal to or greater than $5,000, it would be enough to pay off the loan. However, if the present value is smaller than $5,000, it means the payments will not be sufficient to pay off the loan.

In this case, without specific information about the discount rate used to calculate the present value, we cannot make an exact determination. However, based on the given information, which states that the present value of the payments is smaller than the amount of the loan, it suggests that the payments will not be enough to pay off the credit card debt.

Learn more about discount here: brainly.com/question/31746893

#SPJ11

Answer:4/8 or simplified answer 1/2

Step-by-step explanation:

3/4 + 3/8, first you have to find the highest common factor of 4 and 8.

The answer is 9. The denominator of both side will be 8. Now you ask yourself 4 times what gives you 8 and times the numerator by that number. And do the same for the 8.

6/8 + 3/8= 9/8

9/8 - 5/8= 4/8

The simplified answer is 1/2

Simple linear regression is a statistical technique used to model the relationship between two variables by fitting a straight line to the data. It provides a way to predict or estimate the value of one variable (dependent variable) based on the value of another variable (independent variable).

In simple linear regression, the relationship between the independent variable (x) and the dependent variable (y) is represented by a straight line. The goal is to find the best-fitting line that minimizes the differences between the observed values of the dependent variable and the predicted values from the regression line.

A graph illustrating simple linear regression includes the scatterplot of the data points, the regression line, and the residuals. The scatterplot shows the individual data points with the independent variable on the x-axis and the dependent variable on the y-axis. The regression line is the line that best fits the data, minimizing the sum of the squared residuals.

Residuals are the vertical distances between the observed data points and the regression line. They represent the differences or errors between the actual values and the predicted values. By examining the residuals, we can assess how well the regression line fits the data. If the residuals are randomly scattered around zero, it suggests that the linear regression model is appropriate. If there is a pattern or systematic deviation in the residuals, it indicates that the model may not be capturing the underlying relationship accurately.

The regression line is constructed by minimizing the sum of the squared residuals, which is known as the least squares method. This ensures that the line represents the best linear approximation of the relationship between the variables.

Learn more about linear regression here:

https://brainly.com/question/2120341

#SPJ11

Answer:

B

Step-by-step explanation:

The sections of the parallel roads split by the transversals are in proportion, that is

\(\frac{350}{300}\) = \(\frac{first}{1650}\) ( cross- multiply )

300 first = 577500 ( divide both sides by 300 )

first = 1925 ft

Thus

Elm st → Maple st = 1925 + 350 = 2275 ft → B

let's solve for y :

Answer:

x=-2+y

Step-by-step explanation:

4=2y-2x

switch sides

2y-2x=4

subtrackt 2y from both sides

2y-2x-2y=4-2y

simplify

-2x=4-2y

divide both sides by -2

-2x/-2=4/2-2y/2

simplify

x=-2+y