Let B be the amount Beatrice charges per hour per child
Let x be the number of hours
Let n be the number of children
a)total amount Beatrice charges = T = B*x*n - 10
b)n =4 and T = 100
100 = B*x*4 -40
x = 35/B
c)Let S be the amount she has t o pay to her sister
n = 3 and x = (4+4+5) = 13
so, 13*B*3 -30 -S = 100
S = 39B - 130
Find the supplementary angle of 116 degrees.
Find the sum of the arithmetic sequence. 5, 7, 9, 11, ..., 23
The answer is 140, you just add them up and it goes by 2.
What percent is 6 out of 7?
A winter sport passed at Wood Middle school costs $15. A stydent without a pass must pay $1.75 for each event. How many events would a student have to attend to pass a better deal?
Answer:
9
Step-by-step explanation:
15 divided by 1.75 equals 9.
And in order to double check, we multiply 9 and 1.75 together which equals 15.75.
jimmy had 8 boxes with 3 cars in each box. if jimmy wanted to give each of his 4 friends an equal number of cars, how many cars would each friend get?
What is the value of x in the diagram below?
A 30
B 60
C 90
D 120
could you please explain how you get the answer thank you so much.
A line with a slope of 2 passes through (3,9) Which choice is an equation of this line?
The equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
The equation of a line with slope (m) passing through a point (x₁, y₁) is given by the point-slope form:
y - y₁ = m(x - x₁)
The slope (m) is 2, and the point (x₁, y₁) is (3, 9). Plug these values into the equation:
y - 9 = 2(x - 3)
Now, you can simplify this equation:
y - 9 = 2x - 6
To isolate y, add 9 to both sides:
y = 2x - 6 + 9
y = 2x + 3
Therefore, the equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
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What is the greatest common factor of 4k , 18k4, and 12
Answer:
2
Step-by-step explanation:
The greatest common factor of whole numbers is the largest number that is a factor of all numbers. That is, it is the largest number that can divide all numbers.
In this case, the largest number that divide all the numbers is 2, who can divide 4, 18 and 12.
So:
[tex](4k, 18k^{4} ,12)= 2(2k,9k^{4} , 6)[/tex]
Part A: Solve -np 70 < 40 for n. Show your work. (4 points)
Part B: Solve 4w -7k 28 for k. Show your work. (6 points)
Click on the graph to choose the best match of the graphed quadratic equation. F(x) = x 2 + 4x
The required graph of the quadratic function is the parabola shown in the attachment.
Given that,
To determine the graph to the best match of the graphed quadratic equation. F(x) = x² + 4x.
A parabola is a cross-section cut out of the cone and represented by an equation.
What is a graph?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The given equation represents the parabola with vertex at (-2, - 5).
and a graph of the parabola is attached below.
Thus, the required graph of the quadratic function is the parabola shown in the attachment.
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You have a bag of 42 candies you want to give to your 6 friends. the company that makes the candies guarantees that exactly 6 of the candies in the bag are red, the most delicious color. anyone who doesn't get a red candy will be so upset that they will stop being your friend! but the candies are in identical wrappings, so you are forced to give each friend 7 candies and hope for the best. what's the probability you lose one or more friends?
Final answer:
To calculate the probability of losing one or more friends, we need to calculate the probability that a friend does not get a red candy and multiply it by the number of friends. The probability is 0.458.
Explanation:
To answer this question, we need to calculate the probability that at least one friend will not get a red candy.
First, let's calculate the probability that a friend does not get a red candy. There are 42 candies in the bag and 6 of them are red. So, the probability that a friend does not get a red candy is (42-6)/42 = 36/42 = 6/7.
Since each friend gets 7 candies, the probability that one friend does not get a red candy is (6/7)^7, because each candy is independent. Finally, since there are 6 friends, we multiply the probability by 6 to get the probability that at least one friend does not get a red candy: 6 * (6/7)^7 = 0.458 (rounded to 3 decimal places).
A class had 30 pupils at the beginning of this school term, but now has 5 more pupils. What is the percent of increase?
A ___________ is a line segment that connects the center of a circle to a point on that circle.
A) radius
B) chord
C) diameter
D) obtuse angle
The current population of a city can be represented by p. the population is expected to increase by 6.5% next year. Write a expression in simplest form that represents the expected population next year
The expression in the simplest form that represents the expected population next year will be 1.065p.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The ongoing populace of a city can be addressed by p. the populace is supposed to increment by 6.5% one year from now.
The expression in the simplest form that represents the expected population next year will be given as,
⇒ p(1 + 0.065)
⇒ 1.065p
The expression in the simplest form that represents the expected population next year will be 1.065p.
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The circumference of a circle is 60π cm. What is the length of an arc of 140°? 11.7π cm 16.1π cm 23.3π cm 29.5π cm
Answer:
c = 23.3
Step-by-step explanation:
Answer:
[tex]23.3 \pi[/tex] cm
Step-by-step explanation:
Circumference of circle = [tex]2 \pi r[/tex]
The circumference of a circle is 60π cm.
So, [tex]2 \pi r=60 \pi[/tex]
[tex]2r=60[/tex]
[tex]r=30[/tex]
Formula of length of arc = [tex]2 \pi r \times \frac{\theta}{360}[/tex]
Length of arc = [tex]2 \pi \times 30 \times \frac{140}{360}[/tex]
Length of arc = [tex]23.3 \pi[/tex]
So, Option C is true
Hence Length of arc is [tex]23.3 \pi[/tex] cm
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify [Q - R] + [S - T].
Answer: [tex][Q - R] + [S - T]=10m+7n-14[/tex]
Step-by-step explanation:
Given : [tex]Q = 7m + 3n[/tex],
[tex]R = 11 -2m[/tex],
[tex]S = n + 5[/tex], and
[tex]T = -m - 3n + 8[/tex]
Now , [tex]Q-R= 7m + 3n-(11 - 2m)[/tex]
[tex]Q-R= 7m +3n-11+2m[/tex] [ ∵ (-)(+)=(-) and (-)(-)=(+)]
[Note : when -1 is outside the parenthesis it indicates that -1 should be multiplied with each of the terms present inside the parenthesis .]
[tex]Q-R= 9m +3n-11[/tex] [Combine like terms.]
[tex]S-T=n + 5-(-m - 3n + 8)[/tex]
[tex]S-T=n + 5+m+3n-8[/tex] [ ∵ (-)(+)=(-) and (-)(-)=(+)]
[tex]S-T=4n +m-3[/tex] [Combine like terms.]
Now, [tex][Q - R] + [S - T]=[9m +3n-11]+[4n +m-3][/tex]
[tex]=9m +3n-11+4n+m-3[/tex]
[tex]=10m+7n-14[/tex] [combine like terms]
Hence, [tex][Q - R] + [S - T]=10m+7n-14[/tex]
Assume that the probability of error-free transmission of a message over a communication channel is . if a message is not transmitted correctly, a retransmission is initiated. this procedure is repeated until a correct transmission occurs. such a channel is often called a feedback channel. assume that successive transmissions are independent.
a. what is the probability that no retransmissions are required? (note that the number of retransmissions is the number of transmissions minus one.)
Answer:
Let the probability of error-free transmission of a message over a communication channel is P.
Then the Probability of Retransmission is =1-P
Now the question is Probability when no retransmission is required
= Probability of error free transmission in first attempt
=P
Now , suppose after first failure error free transmission takes place.
Since events are independent.
∵P[error free transmission after a failure ]= P[1-P]
If after two attempts error free transmission takes place
then P[ error free transmission after two failures]= P [1-P]²
So, For after n failures
P[error free transmission after n failure]=P[tex][1-p]^n[/tex]
24 red marbles is 40% of how many marbles
Answer:
60 marbles
Step-by-step explanation:
Given: 24 red marbles is 40% of how many marbles
Let number of marbles be x
"24 red marbles is 40% of how many marbles"
24 = 40% of x
solve for x
First change % to decimal
24 = 0.40x
Division property of equality, divide by 0.04 both sides
x = 24÷0.40
x = 60
Hence, 40% of 60 is 24
Which expressions describe the area of the shaded region? Select all that apply. A rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles. An area that includes 9 smaller rectangles and is the intersection of 3 of the 12 columns and 3 of the 6 rows is shaded. A. 3 12 × 3 6 312×36 B. 3 10 × 1 2 310×12 C. 1 4 × 1 2 14×12 D. 1 4 × 1 3 14×13 E. 4 12 × 3 6 412×36
The expressions describing the area of the shaded region is 1/2 × 1/4
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, a rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles.
We need to find the expressions for the area of the shaded region,
So, we have,
The height is 6 and the length is 12
The shaded part is 3 boxes by 3 boxes
Therefore, we can write =
3/6 × 3/12 = 1/2 × 1/4
Hence, the expressions describing the area of the shaded region is 1/2 × 1/4
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Wilt and bill, two basketball players, are having a free throw shooting contest. wilt is known to make 75% of his free throws, and bill is known to hit 85% of his free throws. each of them takes 50 shots. assuming that the shots are independent, what is the probability that bill hits a higher percentage of his shots than wilt?
The probability Bill hits a higher percentage than Wilt in free throws is approximately 0.0085, or 0.85%.
To find the probability that Bill hits a higher percentage of his shots than Wilt, we can use the concept of binomial distributions.
Step 1 :Let's denote:
- [tex]\( W \)[/tex] as the number of successful shots Wilt makes out of 50,
- [tex]\( B \)[/tex] as the number of successful shots Bill makes out of 50.
Since Wilt makes 75% of his free throws and Bill makes 85% of his free throws, we can calculate the expected number of successful shots for each:
- For Wilt: [tex]\( E(W) = 50 \times 0.75 = 37.5 \)[/tex]
- For Bill: [tex]\( E(B) = 50 \times 0.85 = 42.5 \)[/tex]
Now, we can use the normal approximation to the binomial distribution to calculate the probability that Bill hits a higher percentage of his shots than Wilt. We'll assume that both distributions are approximately normal due to the central limit theorem.
The standard deviation for each player's distribution can be calculated as:
- For Wilt: [tex]\( \sigma_W = \sqrt{n \times p_W \times (1-p_W)} = \sqrt{50 \times 0.75 \times 0.25} \)[/tex]
- For Bill: [tex]\( \sigma_B = \sqrt{n \times p_B \times (1-p_B)} = \sqrt{50 \times 0.85 \times 0.15} \)[/tex]
Step 2 :Now, we can calculate the probability using a normal distribution:
[tex]\[ P(B > W) = P\left(Z > \frac{{E(B) - E(W)}}{{\sqrt{\sigma_B^2 + \sigma_W^2}}}\right) \][/tex]
Where [tex]\( Z \)[/tex] is a standard normal random variable.
Calculating:
[tex]\[ P(B > W) = P\left(Z > \frac{{42.5 - 37.5}}{{\sqrt{50 \times 0.85 \times 0.15 + 50 \times 0.75 \times 0.25}}}\right) \][/tex]
[tex]\[ P(B > W) = P(Z > 2.3717) \][/tex]
Using a standard normal distribution table or calculator, we find that [tex]P(Z > 2.3717) \approx 0.0085 \).[/tex]
So, the probability that Bill hits a higher percentage of his shots than Wilt is approximately 0.0085, or 0.85%.
Which statements are true about the regular polygon? Check all that apply. The sum of the measures of the interior angles is 900°. Each interior angle measures 108°. All of the angles are congruent. The polygon is a regular hexagon. The sum of the measures of the interior angles is 180(5 – 2)°.
Answer: 2,3,5
Step-by-step explanation:
Sales of tablet computers at ted glickman's electronics store in washington,
d.c., over the past 10 weeks are shown in the table below: week 1 2 3 4 5 6 7 8 9 10 demand 19 23 28 38 25 29 37 20 26 30 a) the forecast for weeks 2 through 10 using exponential smoothing with alpha = 0.60 and a week 1 initial forecast of 19.0 are (round your responses to two decimal places):
Minnie and Tori combined ate nine pieces of the wedding cake Mindy ate 3 pieces of the wedding cake Tori have one fourth of the total kick write an expression to determine how many pieces of cake C there was in total
Use the drop-down menus to choose steps in order to correctly solve
5m – 8 = 3m + 8 for m.
Answer:
m=8
Step-by-step explanation:
on imagine 2021
Consider the function f(x) = x2 + 12x + 11. x-intercepts: 0 = x2 + 12x + 11 0 = (x + 1)(x+ 11) y-intercept: f(0) = (0)2 + 12(0) + 11 What are the intercepts of the function? The x-intercepts are . The y-intercept is .
Answer:
the x-intercepts are (-1,0) and (-11,0), the y-intercept is (0,11).
A researcher measured the heights of forty high-school students. The measurements are recorded here.
Heights (in inches)
58 59 60 60 60 61 61 61 61 62
62 62 62 62 62 63 63 63 64 65
67 67 68 68 68 68 69 69 70 70
70 71 71 71 71 71 72 73 74 76
If Alyssa's height is in the 45th percentile within the group, what is her height in inches?
Answer:
64
Step-by-step explanation:
i just know
A deck of cards has 3 blue, 4 black, and 6 purple cards. Draw 2 cards without replacing any cards. What is the probability of both cards being blue?
How do you write the equation of Mary has 10 roses John has 2 less
Akule borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what period of time did Akule borrow money
Using the simple interest formula I = PRT, it is calculated that Akule borrowed $1500 at an annual interest rate of 12% for 1.5 years to pay $270 in interest.
Explanation:The subject of this question is Mathematics, specifically focusing on simple interest calculation. To find out the period of time Akule borrowed money for, we can use the simple interest formula I = PRT, where I is the interest paid, P is the principal amount borrowed, R is the annual interest rate, and T is the time in years. Akule paid $270 in interest on a $1500 loan at 12% annual simple interest. Using the formula, we solve for T as follows:
T = I / (P × R)
T = $270 / ($1500 × 0.12)
T = $270 / $180
T = 1.5 years
Therefore, Akule borrowed the money for 1.5 years.
Akule borrowed the money for 0.18 years.
Explanation:To find the period of time Akule borrowed the money, we can use the formula:
Interest = Principal × Rate × Time
Given that Akule paid $270 in interest and borrowed $1500 at an annual simple interest rate of 12%, we can plug in these values into the formula:
270 = 1500 × 0.12 × Time
Simplifying the equation, we get:
0.12 × Time = 270 / 1500
Time = (270 / 1500) / 0.12
Time = 0.18 years
Hence, Akule borrowed the money for 0.18 years.
the ratio of pens to pencils in Carlos case 4:5 he has 16 pens how many pencils do Carlos have