Pamela is 15 years younger than Jiri. The sum of their ages is 55. What is Jiri's age?

If a basketball player has a 70% accuracy rate for making free throws. The probability that this player misses his first free throw, but makes the second one is 0.21.

The probability of making a free throw is 0.7, so the probability of missing a free throw is 0.3.

Let X be the number of trials (free throws) until the first success (a made free throw). Since we want to know the probability of missing the first free throw and making the second one, we want to find P(X = 2).

Using the geometric distribution formula, we have:

P(X = 2) = (1 - p)^(k-1) * p

where:

p is the probability of success (making a free throw)

k is the number of trials (2 in this case), and (1 - p)^(k-1) is the probability of having k-1 failures (missing the first free throw) followed by one success (making the second free throw).

Plugging in the values, we get:

P(X = 2) = (1 - 0.7)^(2-1) * 0.7

= 0.3 * 0.7

= 0.21

Therefore, the probability  is 0.21 (rounded to the hundredths place).

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The mistake is on the second line of her work.

She wrote -2x + 4 when it should have been -2x -4 because she multiplied -2 by 2 the 4 would be negative: -2 x 2 = -4

Then adding 4 to the 7, x would be 11

Answer: She’s wrong because on the second line, she should’ve put -2x-4 instead of -2x+4 . X equals 11 because if you add 4 to 7 that’s what you’ll get ,

Step-by-step explanation:

Answer:

Domain { -3,-1,6,9}

Step-by-step explanation:

The domain is the input values

Domain { -3,-1,6,9}

Answer:

domain of relation are {-3, -1 ,6, 9}

Answer:

0=0

Step-by-step explanation:

both sides are true for the equation

Answer:

your question is wrong

because the x end up cancelling each other

Answer:

5

Step-by-step explanation:

The length KL is 8 units

The value of x is undefined

The length KL is 12 units

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

The rhombus

Also, we have

DK = 8

A rhombus is a quadrilateral with all sides equal.

So, we have

KL = 8

Here, we have

SKAL = 2x - 8

There is no point S on the rhombus

This means that

x = undefined

Here, we have

DM = 5y + 2 and DK = 3y + 6

A rhombus is a quadrilateral with all sides equal.

So, we have

5y + 2 = 3y + 6

Evaluate

2y = 4

Divide

y = 2

So, we have

KL = 5 * 2 + 2

KL = 12

Hence, the length KL is 12 units

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The dimensions of the product matrix of two of these matrices is BD = 2 * 1 , CA = 1 * 3 and DC = 2 * 3 .

Given :

The dimension of BD :

B dimensions = ( 2 * 2 )

D dimensions = ( 2 * 1 )

Product of BD dimensions = Numbers of rows of B * number of columns in D

= 2 * 1

The dimension of CA :

C dimensions = ( 1 * 3 )

A dimensions = ( 3 * 3 )

Product of CA dimensions = Numbers of rows of C * number of columns in A

= 1 * 3

The dimension of DC :

D dimensions = ( 2 * 1 )

C dimensions = ( 1 * 3 )

Product of CA dimensions = Numbers of rows of D * number of columns in A

= 2 * 3

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Since the pump is emptying the water at a constant rate of 20 ft³/min, then we can set the following equation:

Answer:

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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Answer:

They are collinear if they are on the same line

The area of the shaded shape is 62.5cm^2.

To find the area of the shaded shape, we need to break it down into simpler shapes that we can calculate the area of. From the image, we can see that the shape is composed of a rectangle and two right-angled triangles.

First, we need to find the dimensions of the rectangle. Since the shape has vertical and horizontal lines of symmetry passing through its center, we know that the rectangle is divided into four equal parts.

Therefore, the length of the rectangle is twice the length of one of the triangles, which is 5cm. So, the length of the rectangle is 2 x 5cm = 10cm. The width of the rectangle is also 5cm.

Next, we need to find the area of each of the triangles. We know that the base of each triangle is 5cm, and the height is half of the width of the rectangle, which is 2.5cm. Therefore, the area of each triangle is:

0.5 x base x height = 0.5 x 5cm x 2.5cm = 6.25cm^2

So, the total area of the two triangles is 2 x 6.25cm^2 = 12.5cm^2.

Finally, we can find the area of the shaded shape by adding the area of the rectangle and the area of the triangles:

Area = rectangle area + triangle area = 10cm x 5cm + 12.5cm^2 = 62.5cm^2.

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Answer:

C. 16 feet.

Step-by-step explanation:

How to find the maximum height of a projectile

if α = 90°, then the formula simplifies to: hmax = h + V₀² / (2 * g) and the time of flight is the longest.  

if α = 45°, then the equation may be written as:  

if α = 0°, then vertical velocity is equal to 0 (Vy = 0), and that's the case of horizontal projectile motion.

Answer:

76%

Step-by-step explanation:

57/75

(57 X 100)/ 75

5700/75

1900/25

76/1

76

Answer:

22222

Step-by-step explanation:

Total milligrams

COST PER MG:-

Answer:

$3.17

Step-by-step explanation:

1 pill = 3 mg

⇒ 45 pills = 45 × 3 = 135 mg

45 pills = $427.95

⇒ 135 mg = $427.95

⇒ 1 mg = $427.95 ÷ 135 = $3.17

Answer:

6

Step-by-step explanation:

9*2/3=3*2=6 (Cross Cancelling)

Answer: 6

Step-by-step explanation:

So basically, you can figure this out by turning 9 into a fraction, which is \(\frac{9}{1}\). So,

\(\frac{9}{1}\) x \(\frac{2}{3}\) and multiply it across. So 9 x 2 is 18, and 1 x 3 is 3, so that gets us to \(\frac{18}{3}\). And since this is an improper fraction, we divide 18 by 3 to get 6! Hope this helps! :)

Answer:

You will have earned $113 in interest.

Step-by-step explanation:

After investing for 4 years at 3% interest, your initial investment of $900 will have grown to $1,013.

To find the amount you need to invest, we can use the formula for simple interest:

\(\displaystyle\sf \text{{Interest}} = \text{{Principal}} \times \text{{Rate}} \times \text{{Time}}\)

Here, the principal is the amount you need to invest, the rate is 3% (or 0.03 as a decimal), and the time is 4 years. We can rearrange the formula to solve for the principal:

\(\displaystyle\sf \text{{Principal}} = \frac{{\text{{Interest}}}}{{\text{{Rate}} \times \text{{Time}}}}\)

Plugging in the given values, we get:

\(\displaystyle\sf \text{{Principal}} = \frac{{900}}{{0.03 \times 4}}\)

Simplifying further:

\(\displaystyle\sf \text{{Principal}} = \frac{{900}}{{0.12}}\)

Calculating the division:

\(\displaystyle\sf \text{{Principal}} = 7500\)

Therefore, you will need to invest $7500 at 3% to have earned $900 in interest in 4 years.

Answer:259,200 seconds

Step-by-step explanation:

24 hours in one day

1 hour= 60 minutes

1 minute =60seconds

60x60=3,600

3,600x24=86,400 seconds

86,400x3(days)=259,200 seconds

The reasons that complete the statements are:

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

Triangles = RST, and TUR

From the question, we have the following given parameters

∠SRT ≅ ∠UTR

This means that

Statement 2: ∠SRT ≅ ∠UTR ------ Given

At this point, we have

RS ≅ TU --- Congruent side (S)

∠SRT ≅ ∠UTR ------ Congruent angle (A)

RT ≅ TR --- Congruent side (S)

When these congruent sides and angles are combined, we have

SAS congruence property

The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent

Hence, the additional information on the congruency of the triangles are Given and SAS congruence property

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The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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The approximate area of the property is;

Here, we want to calculate the area of the property

Firstly, we can see that the farm is divided into two shapes (two triangles actually)

By finding the areas of the two triangles, adding tehm up, we will have the area of the farm

Firstly, we need to get all the sides of the triangles

Let us start with the triangle below

It is simply the length of the diagonal QS

We can find this by the use of cosine rule

We have this as;

Now, by using this calculated diagonal, we can get the missing side of the top triangle

We have the missing side calculated as follows;

So, we now use Heron's formula for each of the two triangles before adding up

For triangle QPS, we have;

For triangle QRS, we have;

The area of the sheep farm is the sum of both areas

We have this as;

The function (f) gives us the total amount of money Guadalupe makes in a week, in terms of the number of hours she works as a waitress (x) is h(x) = -4.75x + 495

Let's start by defining the functions:

f(x) = amount of money Guadalupe makes as a waitress for x hours

g(x) = amount of money Guadalupe makes as a tutor for the remaining (30 - x) hours, given that she has already worked x hours as a waitress

h(x) = total amount of money Guadalupe makes in a week, given that she has worked x hours as a waitress and (30 - x) hours as a tutor.

To find the amount of money Guadalupe makes as a waitress for x hours, we can simply multiply her hourly wage ($11.75) by the number of hours she works:

f(x) = 11.75x

To find the amount of money Guadalupe makes as a tutor for the remaining (30 - x) hours, we can use the same approach, but with her tutor hourly wage ($16.50):

g(x) = 16.5(30 - x)

Note that we are using (30 - x) instead of just x, since the number of hours she can work as a tutor is limited by the number of hours she has already worked as a waitress.

Finally, to find the total amount of money Guadalupe makes in a week, we simply add up the amount of money she makes as a waitress and the amount of money she makes as a tutor:

h(x) = f(x) + g(x)

h(x) = 11.75x + 16.5(30 - x)

h(x) = 11.75x + 495 - 16.5x

h(x) = -4.75x + 495

So the function h(x) gives us the total amount of money Guadalupe makes in a week, in terms of the number of hours she works as a waitress (x).

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The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The area of the sector is approximately 9.25 ft².

We have,

The formula for the area of a sector.

A = (θ/360°) × πr²

where A is the area of the sector, θ is the central angle in degrees, and r is the radius.

Substituting the given values.

A = (40°/360°) × 3.14 × (16.7 ft)²

A = 0.1111 × 3.14 × 278.89 ft²

A = 9.2465 ft²

Rounding to the nearest hundredth.

A ≈ 9.25 ft²

Therefore,

The area of the sector is approximately 9.25 ft².

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The solution of the given question will be the probability that at least 10 eggs are unbroken is 0.01.

Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain. In between, probabilities are expressed as fractions or decimals, with higher probabilities indicating a greater likelihood of the event occurring. Probability is used extensively in fields such as mathematics, statistics, physics, economics, and engineering to model uncertain events and to make predictions based on those models.

(a) Since the sum of probabilities for all possible values of y must equal 1, we have:

0.63 + 0.22 + 0.10 + 0.04 + p(4) = 1

Solving for p(4), we get:

p(4) = 1 - 0.63 - 0.22 - 0.10 - 0.04 = 0.01

Therefore, p(4) = 0.01.

(b) p(1) = 0.22 represents the probability that a randomly selected carton of eggs will have exactly one broken egg. It can also be interpreted as the proportion of cartons in this population that have exactly one broken egg.

(c) P(y ≤ 2) is the probability that the carton contains at most two broken eggs. We can calculate this probability by adding the probabilities of y = 0, y = 1, and y = 2:

P(y ≤ 2) = p(0) + p(1) + p(2) = 0.63 + 0.22 + 0.10 = 0.95

This means that in the long run, 95% of cartons in this population will have at most two broken eggs. It can also be interpreted as the proportion of eggs in any two cartons from this population that will be broken.

(d) P(y < 2) is the probability that the carton contains fewer than two broken eggs. This means that the only possible values for y are 0 or 1, so we have:

P(y < 2) = P(y = 0) + P(y = 1) = 0.63 + 0.22 = 0.85

This probability is smaller than the probability in part (c) because P(y ≤ k) is always greater than or equal to P(y < k) for any value of k, since P(y = k) is non-negative.

(e) The value of y represents the number of broken eggs, so if a carton contains exactly 10 unbroken eggs, then it must have 2 broken eggs, since there are 12 eggs in a carton. Therefore, the probability of a carton having exactly 10 unbroken eggs is equal to the probability of y = 2, which is 0.10.

(f) To calculate the probability that at least 10 eggs are unbroken, we need to find the sum of the probabilities for y = 10, y = 11, and y = 12, since these correspond to the cases where at least 10 eggs are unbroken:

P(10 ≤ y ≤ 12) = P(y = 10) + P(y = 11) + P(y = 12) = 0 + 0 + 0.01 = 0.01

Therefore, the probability that at least 10 eggs are unbroken is 0.01.

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The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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The percentage of our new facility's seating is full will be 76%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

Our new training room can seat 150 employees.

If 6 tables consisting of 6 chairs are now taken.

Then the number of occupied seats by tables will be

⇒ 6 x 6

⇒ 36

Then the percentage of our new facility's seating is full will be

P = [(150 - 36) / 150]  x 100

P = (114/150) x 100

P = 0.76 x 100

P = 76%

The percentage of our new facility's seating is full will be 76%.

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Answer:

(D

Step-by-step explanation:

Calculator in the picture below.

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