This Venn diagram shows the pizza topping preferences for 9 students. Let event A = The student likes pepperoni. Let event B = The student likes olives. What is P(A or B)?​

Answer:

  -21 degrees

Step-by-step explanation:

Dropping 6 degrees per hour, the temperature drops 5×6 = 30 degrees in 5 hours. Starting at 9 degrees and dropping 30, the temperature becomes -21 degrees at 9 am.

Answer:

The probability is 0.74719

Step-by-step explanation:

Let's start defining the random variable X.

X : ''Number of children with hyperlipidemia out of 12 children''

X can be modeled as a binomial random variable.

X ~ Bi (n,p)

Where n is the sample size and p is the ''success probability''.

We defining as a success to find a child that has hyperlipidemia.

The probability function for X is :

[tex]P(X=x)=(nCx).p^{x}.(1-p)^{n-x}[/tex]

Where nCx is the combinatorial number define as :

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

We are looking for [tex]P(X\geq 3)[/tex]

[tex]P(X\geq 3)=1-P(X\leq 2)[/tex]

[tex]P(X\geq 3)=1-[P(X=0)+P(X=1)+P(X=2)][/tex]

[tex]P(X\geq 3)=1-[(12C0)0.3^{0}0.7^{12}+(12C1)0.3^{1}0.7^{11}+(12C2)0.3^{2}0.7^{10}][/tex]

[tex]P(X\geq 3)=1-(0.7^{12}+0.07118+0.16779)=1-0.25281=0.74719[/tex]

There is a probability of 0.74719 that at least 3 children are hyperlipidemic.

To find the probability that at least 3 out of the 12 children are hyperlipidemic, we can use the binomial probability formula. The probability is 36.21% or 0.3621.

To find the probability that at least 3 out of the 12 children are hyperlipidemic, we need to use the binomial probability formula. The probability of success is 30% or 0.3 (since 30% of children are hyperlipidemic), and the probability of failure is 1 - 0.3 = 0.7.

The formula for the binomial probability is P(X >= k) = 1 - P(X < k), where X follows a binomial distribution with n trials (12 children in this case) and probability of success p (0.3).

To find P(X < k), we need to calculate the probabilities for X = 0, 1, and 2 children being hyperlipidemic and then sum them up.

Summing up these probabilities, we get P(X < 3) = 0.0687 + 0.2332 + 0.3361 = 0.6379

Finally, the probability of at least 3 children being hyperlipidemic is P(X >= 3) = 1 - P(X < 3) = 1 - 0.6379 = 0.3621 or 36.21%.

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Answer:

Option C.

Step-by-step explanation:

Given information

[tex]n_1=1563[/tex] and [tex]n_2=579[/tex]

[tex]x_1=61[/tex] and [tex]x_2=15[/tex]

Using the given information we get

[tex]p_1=\dfrac{x_1}{n_1}=\dfrac{61}{1563}\approx 0.039[/tex]

[tex]p_2=\dfrac{x_2}{n_2}=\dfrac{15}{579}\approx 0.026[/tex]

The formula for confidence interval for p_1 - p_2 is

[tex]C.I.=(p_1-p_2)\pm z*\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]

From the standard normal table the value of z* at 95% confidence interval = 1.96.

[tex]C.I.=(0.039-0.026)\pm (1.96)\sqrt{\dfrac{0.039(1-0.039)}{1563}+\dfrac{0.026(1-0.026)}{579}}[/tex]

[tex]C.I.=0.013\pm (1.96)(0.008)[/tex]

[tex]C.I.=0.013\pm 0.016[/tex]

[tex]C.I.=(0.013-0.016,0.013+0.016)[/tex]

[tex]C.I.=(-0.003,0.029)[/tex]

The 95% confidence interval for p_1 - p_2. is (-0.003,0.029).

Therefore, the correct option is C.

Final answer:

The correct 95% confidence interval for the difference in proportions of dizziness between subjects taking Accupril and those not taking it, using the sample data provided, is (0.006, 0.092).

Explanation:

To create a 95% confidence interval for the difference in proportions (p_1 - p_2), where p_1 is the proportion of people who experience dizziness while taking Accupril, and p_2 is the proportion of people experiencing dizziness but not taking Accupril, we use the following formula:

Confidence Interval = (p_hat_1 - p_hat_2) ± Z*sqrt((p_hat_1*(1 - p_hat_1)/n_1) + (p_hat_2*(1 - p_hat_2)/n_2))

Where p_hat_1 and p_hat_2 are the sample proportions, n_1 and n_2 are the sample sizes, and Z is the Z-score corresponding to a 95% confidence level (1.96 for two-tailed tests).

After calculating these proportions and plugging the values into the formula, the confidence interval is (0.006, 0.092).

Hence, the correct answer is option a. (0.006, 0.092).

Answer:

  [tex]\boxed{x=2}[/tex]

Step-by-step explanation:

The equation of a parabola with vertex (h, k) and directrix-to-vertex distance p is given by ...

  (y -k)^2 = 4p(x -h)

The directrix is the line x = (h -p)

Here, we have the vertex at x=5. The distance from the directrix satisfies ...

  12 = 4p

  12/4 = p = 3

So, the directrix is at x = 5 - 3, or x = 2.

_____

The graph shows the given parabola along with the focus and directrix. The dashed lines are intended to show that each of those is in the right place, as the distance from any point on the parabola is the same to the focus and the directrix.

Final answer:

The equation of the directrix of the parabola with the equation (y + 2)² = 12(x - 5) is x = 2.

Explanation:

To find the equation of the directrix of a parabola, we first need to identify the vertex form of the parabola's equation. The given equation of the parabola is (y + 2)² = 12(x - 5). This equation indicates that the parabola opens horizontally to the right since the squared term is (y + 2)² and the x is positive in the standard form of the equation. The vertex of the parabola is at the point (5, -2).

For a parabola in the form (y - k)² = 4p(x - h), where (h, k) is the vertex, the directrix is a vertical line if the parabola opens horizontally. The value of p determines the distance from the vertex to the focus and to the directrix. The given equation can be rewritten as (y + 2)² = 4(3)(x - 5), so here p is equal to 3. Since the parabola opens to the right, the directrix will be to the left of the vertex at a distance of 3 units.

The equation for the directrix is thus a vertical line x = h - p. Plugging the vertex coordinates and p into this formula, we get x = 5 - 3, which simplifies to x = 2. Therefore, the equation of the directrix of the given parabola is x = 2.

Answer:

[tex]\overline{BD}\ and\ \overline{AC}[/tex]  bisect each other is sufficient to Prove  Δ ABE ≅ Δ CDE

Step-by-step explanation:

Given: (if it is given)

[tex]\overline{BD}\ and\ \overline{AC}[/tex]  bisect each other, i.e

AE ≅ CE

BE ≅ DE

To Prove:

Δ ABE ≅ Δ CDE

Proof:

In  Δ ABE and Δ CDE

      AE ≅ CE     …………..{ BD and AC bisect each other at E}

∠ AEB ≅ ∠ CED      ………….{Vertically opposite angles are equal}

     BE  ≅ DE     ……….{ BD and AC bisect each other at E}  

Δ ABC ≅ Δ PQR ….{Side-Angle-Side test} ......PROVED

Answer:

standard deviation is 0.51

Step-by-step explanation:

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1065 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.62 hours with a standard deviation of 0.51

Answer:

x = 1 and x = -3

Step-by-step explanation:

roots are points that y = 0

in two points we have this

x = 1 and x = -3

Explanation:

For the purpose of filling in the table, the BINOMPDF function is more appropriate. The table is asking for p(x)--not p(n≤x), which is what the CDF function gives you.

If you want to use the binomcdf function, the lower and upper limits should probably be the same: 0,0 or 1,1 or 2,2 and so on up to 5,5.

The binomcdf function on my TI-84 calculator only has the upper limit, so I would need to subtract the previous value to find the table entry for p(x).

Final answer:

An azimuth is a horizontal angle measured clockwise from a north base line, used in navigation and surveying to indicate direction. It measures angles from 0° to 360°, starting from the north and moving towards the east, which allows for precise direction determination on the earth's surface. The correct answer is A.

Explanation:

The question, "What is an Azimuth?" pertains to how angles, specifically bearings, are measured in relation to the earth's surface. The correct answer is: 'A. A horizontal angle measured clockwise from a north base line.' An azimuth is essentially a type of bearing used in navigation and surveying to indicate direction. It is a measure of rotation from the north direction towards the east, meaning the angle increases in a clockwise fashion. The concept originates from surveying practices and is crucial for determining directions accurately on the earth's surface.

The use of azimuth in surveying involves specifying angles in degrees from 0° to 360°, starting from north towards east, south, west, and back to north. This precise measurement allows geographers, surveyors, and navigators to determine directions and locations with respect to the north base line, which serves as a universal reference point.

Furthermore, azimuth measurements can distinguish between true north, which is the geographical north pole, and magnetic north, which is dictated by the earth's magnetic field. Despite this distinction, azimuths provide a consistent method for defining bearings across various contexts, making them indispensable in mapping and navigation.

Answer:

ΔDBE≅ΔQAP  (by RHS criteria)

Step-by-step explanation:

Given that, [tex]PQ=DE[/tex], [tex]PB=AE[/tex], [tex]QA[/tex]⊥[tex]PE[/tex]

and [tex]DB[/tex]⊥[tex]PE[/tex]

⇒∠PAQ=90° and ∠EBD=90°(definition of perpendicular lines)

Its given that PB=AE,

subtracting AB on both sides,

we get: PB-AE=AB-AE

         ⇒PA=EB (equals subtracted from equals, the remainders are equals)

Therefore, ΔDBE≅ΔQAP (by RHS criteria)

conditions for congruence:

So, ∡D=∡Q(as congruent parts of congruent triangles are equal)

Answer: The price would be $80 at which supply and demand are equal.

Step-by-step explanation:

Since we have given that

Demand function is given by

[tex]\dfrac{9600}{p}[/tex]

where p is the price of a muffin in cents.

Supply function is given by

[tex]44p-200[/tex]

We need to find the price at which supply and demand are equal.

so, it becomes,

[tex]\dfrac{9600}{p}=44p-200\\\\9600=(4p-200)p\\\\9600=4p^2-200p\\\\2400=p^2-50p\\\\p^2-50p-2400=0\\\\p=80,-30[/tex]

We discarded p = -30 as price cannot be negative.

so, the price would be $80 at which supply and demand are equal.

Answer:

Step-by-step explanation:

The bakery found out that the demand is

D = 9600 / p

Where P is the price of muffins in cents

Daily supply is give as

S=4p — 200 ( I believe it is a typo error, and that is why I used 4p - 200, due to the experience I have with brainly site.)

We want to find the price at which the demand is equal to the supply

It is a very straight forward questions

Demand. = Supply

Then,

D = S

9600 / p = 4p - 200

Cross multiply

9600 = 4p² - 200p

Rearrange to form quadratic equation

4p² - 200p - 9600 = 0

Divide through by 4

p² - 50p - 2400 = 0

Check attachment for solution using formula method to solve quadratic equation

Using factorization

p² - 80p + 30p - 2400 = 0

p(p-80) + 30(p-80) = 0

(p+30)(p-80) = 0

So, it is either p+30 = 0. Or p-80=0

p = -30 or p = 80

Since the price can't be negative,

We are going to discard the negative price.

Then, the price is 80cents per muffins.

The 95% confidence interval for the mean weight of all bags of oranges is calculated using the sample mean and the sample standard deviation. After calculation, we are 95% confident the mean weight is between 9.193 and 9.757 pounds.

To find the 95% confidence interval for the mean weight of all bags of oranges, we first need to calculate the sample mean and sample standard deviation. The sample mean, [tex]\overline{x}[/tex], is the sum of all sample weights divided by the number of samples. In this case, it is (9.3+9.7+9.2+9.7)/4 = 9.475 pounds.

The sample standard deviation, s, is the square root of the sum of the squared differences between each sample weight and the sample mean, divided by the number of samples minus one. The s value here is approximately 0.253 pounds.

For a 95% confidence interval with a sample size of 4, the z-score is 2.776 (obtained from a standard z-table). The margin of error is the z-score multiplied by the standard deviation divided by the square root of the sample size. This is approximately 0.282 pounds. So, the 95% confidence interval is (9.475-0.282, 9.475+0.282) = (9.193, 9.757) pounds.

So we can say that we are 95% confident that the mean weight of all bags of oranges is between 9.193 and 9.757 pounds.

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Answer:

ticket owner loses an average of $0.95 per raffle ticket

Step-by-step explanation:

No profit organization plans to hold a raffle to raise funds for its operation .The expected value in this context is that ticket owner loses an average of $ 0.95

Answer:

B: The ticket owners lose an average of $0.95 per raffle ticket.

Step-by-step explanation:

Answer:

56 and 57

Step-by-step explanation:

The numbers 56 and 57 are values that are very close it is better to estimate 56 and 57 then 6 and 56 and 57

The answer to the teacher's question is that approximately 95% of the sample lies within the range of 45 to 69. This conclusion is based on the features of the normal distribution

The study's results use elements of statistics, with the distribution in question being a normal distribution. A characteristic of a normal distribution is that approximately 95% of measurements will fall within two standard deviations, both above and below the mean. Given that the mean in this case is 57 and the standard deviation is 6, we can calculate the values between which approximately 95% of the sample falls.

Doing the math, we find that: 57 - (2*6) = 45 and 57 + (2*6) = 69. Thus, approximately 95% of the sample lies between the values of 45 and 69.

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The plot of land forms right triangle.

Step-by-step explanation:

Let,

the three sides are a,b and c.

The sum of square of two sides equals to the square of third side. We will consider the larger side as c, therefore,

a= 2000 feet

b= 2100 feet

c= 2900 feet

Using Pythagoras theorem;

[tex]a^2+b^2=c^2\\(2000)^2+(2100)^2=(2900)^2\\4000000 + 4410000 = 8410000\\8410000 feet = 8410000 feet[/tex]

As the three sides satisfy pythagoras theorem, therefore, the plot of land form right triangle.

The plot of land forms right triangle.

Keywords: triangle, pythagoras theorem

Learn more about pythagoras theorem at:

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Answer:

c) Sample parameters are usedto make inferences about population statistics

Step-by-step explanation:

In statistics we use samples to make inferences about population

That is the great advantage of the whole role of distribution. Once you know a particular situation or experiment, that you can associate to one specific distribution and compute parameters, you can obtain from a relative smaller quantity of dataand  with good approximation, inferences about the whole population (that can be conform by a very big numbers of elements)

Answer: D. Sample statistics are used to make inferences about population parameters.

Step-by-step explanation: got it right on edge 23  :)

Answer:

70 standard boxes, 40 deluxe boxes

Step-by-step explanation:

standard: x

deluxe: y

x + y = 110

7x + 11y = 930

Multiply the first equation by 7 and subtract.

7x + 7y = 770

-(7x + 11y = 930)

You get -4y = -160

y = 40

Substitute y into the first equation.

x + 40 = 110

x = 70

Answer: 17.7

Step-by-step explanation:

212.4÷12 = 17.7

Answer: 17.7 miles per gallon

Step-by-step explanation:

Hi, to answer this question we have to divide the number of miles (212.4) by the number of gallons used (12).

Mathematically speaking:

212.4 /12 = 17.7 miles per gallon

17.7 is already rounded to the nearest tenth.

His truck gets  17.7 miles per gallon

Feel free to ask for more if needed or if you did not understand something.

Answer:

Step-by-step explanation:

a) The probability that the hand contains exactly one ace

No of ways of selecting one ace and four non ace would be

=[tex]4C1 (48C4)\\\\= 778320[/tex]

i.e. α=778320

b) the probability that the hand is a flush

No of ways of getting a flush is either all 5 hearts or clubs of spades or dice

= [tex]4(13C5) = 5148[/tex]

ie. β=5148

c)  the probability that the hand is a straight flush

In each of the suit to get a straight flush we must have either A,2,3,4,5 or 2,3,4,5,6, or .... or 9,10, J, q, K

So total no of ways = [tex]=9(13C5) 4\\= 46332[/tex]

γ=46332

The probability of getting a hand with exactly one ace from a standard deck is 748,704/2,598,960. For a flush, the probability is 5,148/2,598,960. For a straight flush, the probability is 40/2,598,960.

The total number of possible five card hands from a standard deck is C(52,5)=2,598,960.

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Answer:

28. a) [tex]-7.3 + 7.4[/tex]

29. c) [tex]3n + 0.18[/tex]

Step-by-step explanation:

Question 28:

Given:

The equation is -9.6 + 9.5 + _________ = 0

In order to solve this, first let us simplify the terms -9.6 + 9.5.

-9.6 + 9.5 = -0.1

So, we are getting the sum of first 2 numbers as -0.1. Now, the result is 0. So, we know that,  -a + a = 0. Therefore, the number that should come in the blanks should be -(-0.1) = 0.1

Now, among all the 4 choices, only choice (a) gives the sum as 0.1 as shown below:

-7.3 + 7.4 = 0.1

The options (b) and (c) has a result of 0 and option (d) sum is -0.1.

Therefore, the correct option is option (a).

Question 29:

Given:

The expression to simplify is given as:

[tex]2n+n+0.18[/tex]

Using commutative property of addition, we add the like terms together. Here, the like terms are [tex]2n\ and\ n[/tex]. So, we add them as shown below:

[tex]2n+1n=(2+1)n=3n[/tex]

Therefore, the given expression is simplified to [tex]3n + 0.18[/tex]. Hence, the correct option is option (c).

Answer:

3/8 left

Step-by-step explanation:

I can't draw a model but I can still give an explanation.

1/2 required to memorize - 1/8 already memorized = 3/8 left

Maybe draw a rectangle with 8 divisions and label the situation.

Devon still needs to memorize 3/8 of his lines. This is determined by converting 1/2 to 4/8 and then subtracting the 1/8 he's already learned, leaving 3/8 of his lines remaining.

Devon aims to memorize 1/2 of his lines and has already memorized 1/8 of them. The task here is to find out how many more lines Devon has left to learn. In terms of fractions, this would involve subtracting the already learnt fraction (1/8) from the total goal (1/2).

Firstly, make sure both fractions have the same denominator, for easy calculation. In this case, you can convert 1/2 to 4/8. Now, subtract what you've already learnt. So 4/8 - 1/8 equals 3/8. That means Devon has 3/8 of his lines left to memorize.

To illustrate this visually, consider a pie representing all of Devon's lines. Cut it into 8 even slices. Four of these slices represent the half that Devon wants to learn. He has already learnt one slice (1/8 of the pie). So, he has three slices (3/8 of the pie) left to learn.

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Answer:16/15^2

Step-by-step explanation:

Answer: 250000 pounds

Step-by-step explanation:

The area of one field is 16 acres and the area of the second field is 1 1/4 times bigger. This means that the area of the second field is

1.25 × 16 = 20 acres.

A barn of wheat on the first field makes up 37 1/2 thousands of pounds per acre. This means that the total wheat on the first field will be the amount of wheat per acre × total number of acres. It becomes

37.5 × 16 = 600 000 pounds of wheat.

On the second, it is 1 2/15 times as much per acre. This means that an acre on the second field contains

17/15( converted 1 2/15 to improper fraction) times the number of wheat per acre on the first field.

Amount of wheat per acre for the second field = 17/15 × 37.5 = 42.5

This means that the total wheat on the second field will be the amount of wheat per acre × total number of acres. It becomes

42.5 × 20 = 850 000 pounds of wheat.

We will subtract the amount of wheat gathered from field 1 from the amount gathered from field 2. It becomes 850000 - 600000 = 250000 pounds of wheat. Therefore,

The amount of wheat gathered from the second field is 250000 pounds more than the amount from the first field

Answer: [tex]LSA=128\ cm^2[/tex]

Step-by-step explanation:

The formula for calcualte the Lateral surface area of a prism is:

[tex]LSA=Ph[/tex]

Where "P" is the perimeter of the base and "h" is the height of the prism.

Notice that the base is a triangle. Since the perimeter is the sum of its sides, you get that this is:

[tex]P=5\ cm+6\ cm+5\ cm\\\\P=16\ cm[/tex]

You can identify in the figure that the height is:

[tex]h=8\ cm[/tex]

Therefore, you can substitute these values into the formula in order to calculate the Lateral surface area of the given prism. This is:

[tex]LSA=(16\ cm)(8\ cm)\\\\LSA=128\ cm^2[/tex]

Answer:

128

Step-by-step explanation:

Final answer:

Using Hooke's Law, the spring constant is calculated from the given force and stretch, which is then used to calculate the work done for a larger stretch. The work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.

Explanation:

To solve this problem, we need to use Hooke's Law, which says that the force needed to stretch or compress a spring is directly proportional to the distance the spring is stretched or compressed from its natural length. The formula for the force on a spring is F = kx, where k is the spring constant and x is the stretch from the natural length.

First, we can find the spring constant using the information given: a force of 7 pounds to stretch the spring 0.4 feet beyond its natural length.

Therefore, the work done in stretching the spring from its natural length to 0.7 feet is approximately 4.29 foot-pounds.

The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2

Given, two points are A(-5, 5) and B(3, -3)

We have to find the perpendicular bisector of segment AB.

Now, we know that perpendicular bisector passes through the midpoint of segment.

The formula for midpoint is:

[tex]\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

[tex]Here x_1 = -5 ; y_1 = 5 ; x_2 = 3 ; y_2 = -3[/tex]

[tex]\text { So, midpoint of } A B=\left(\frac{-5+3}{2}, \frac{5+(-3)}{2}\right)=\left(\frac{-2}{2}, \frac{2}{2}\right)=(-1,1)[/tex]

Finding slope of AB:

[tex]\text { Slope of } A B=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]\text { Slope } m=\frac{-3-5}{3-(-5)}=\frac{-8}{8}=-1[/tex]

We know that product of slopes of perpendicular lines = -1  

So, slope of AB [tex]\times[/tex] slope of perpendicular bisector = -1  

- 1 [tex]\times[/tex] slope of perpendicular bisector = -1  

Slope of perpendicular bisector = 1

We know its slope is 1 and it goes through the midpoint (-1, 1)

The slope intercept form is given as:

y = mx + c

where "m" is the slope of the line and "c" is the y-intercept

Plug in "m" = 1

y = x + c   ---- eqn 1

We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1

1 = -1 + c

c = 2

Now substitute c = 2 in eqn 1

y = x + 2

Thus y = x + 2 is the required equation in slope intercept form

Answer:

g=1

Step-by-step explanation:

Given equation is \[−3+5+6g=11−3g\]

Simplifying, \[2+6g=11−3g\]

Bringing all the terms containing g to the left hand side and the numeric terms to the right hand side,

\[6g + 3g=11−2\]

=> \[(6 + 3)g=9\]

In other words, \[g=\frac{9}{9}\]

Or, g = 1

The given equation is satisfied for g=1.

Validation:

Left hand side of the equation: -3+5+6 = 8

Right hand side of the equation: 11-3 = 8

Answer:

2,692 cans of tomato soup were sold in January and July

Step-by-step explanation:

The number of cans of soup sold in January = 1346

Store sold same number of soup cans in July.

⇒The number of cans of soup sold in July = 1346

So, the total soup cans sold in January and July

=  Sum of soup cans sold in both months

=  1346 +  1346

=2,692

Hence, 2,692 cans of tomato soup were sold in January and July.

Step-by-step explanation:

Let [tex]f(x)[/tex] be the number of shares in [tex]x[/tex] days.

Let the function [tex]f(x)=ab^{x}[/tex].

It is given that each friend shares with three friends the next day.

So,[tex]f(x)=3\times f(x-1)[/tex]

substituting [tex]f(x)=ab^{x}[/tex]

[tex]ab^{x}=3\times ab^{x-1}[/tex]

So,[tex]b=3[/tex]

Given that at day [tex]0[/tex],there are [tex]2[/tex] shares.

So,[tex]f(0)=2[/tex]

[tex]a3^{0}=2[/tex]

[tex]a=2[/tex]

So,[tex]f(x)=2\times 3^{x}[/tex]

Answer:

The probability that the student selected will be one who both walks to school and has been late to school at least once is = 0.15 or 15%

Step-by-step explanation:

From the question given, we find the probability that the student selected will be one who both walks to school and has been late to school at least once

Let,

B = Event that student walk to school

C = Event that student have been late to school at least once.

So,

P(B) = 0.40 , P(C) = 0.32

P(C | B) = 0.375

We apply the  multiplication rule,

P(B and C) = P(C | B) * P(B)

= 0.375 * 0.40

= 0.15 or 15%

Ronna collected [tex]12\frac{3}{4}[/tex] bags of clothes

Step-by-step explanation:

Tristan and Ronna are collecting clothes for a clothing drive

We need to find how many bags of clothes  Ronna collected

∵ Ronna collected 3 times as many clothes as Tristan did

- That means Ronna collected 3 × the amount that Tristan did

∵ Tristan collected [tex]4\frac{1}{4}[/tex] bags

- Multiply the amount of Tristan by 3 to find the amount of Ronna

∴ Ronna collected = 3 × [tex]4\frac{1}{4}[/tex]

Change the mixed number to improper fraction

∵ [tex]4\frac{1}{4}[/tex] = [tex]\frac{(4*4)+1}{4}=\frac{17}{4}[/tex]

∴ Ronna collected = 3 × [tex]\frac{17}{4}[/tex]

∴ Ronna collected = [tex]\frac{51}{4}[/tex]

Change the improper fraction to mixed number by divide 51 by 4

∵ 51 ÷ 4 = 12 and reminder 3 (4 × 12 = 48 and 51 - 48 = 3)

∴ [tex]\frac{51}{3}=12\frac{3}{4}[/tex]

∴ Ronna collected = [tex]12\frac{3}{4}[/tex] bags of clothes

Ronna collected [tex]12\frac{3}{4}[/tex] bags of clothes

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