The spinner of Maddi's game is an illustration of probability, and it is expected that the number of spins is 28
How to determine the expected number of vowels?The number of sections in the spinner is given as:
Sections = 4
The letter C is given as:
Letter C = 1
The expected appearance of letter C is given as:
Expected appearance = 7
The expected number of letter C is calculated using
Expected = Letter C/Sections * Number of spins (n)
So, we have:
7 = 1/4 * (n)
Multiply both sides by 4
n = 28
Hence, it is expected that the number of spins is 28
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Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Hello!
The distance, d, is less than 200 miles.
B. d > 200
Which is the graph of the function f/x )= x 2 2x 3?; Which graph represents the function f/x )= 4 x?; How do you find a function on a graph?; Which is one of the transformations applied to the graph of f/x )= x2 to change it into the graph?
The graph of the function f(x) = x² + 2x + 3 is a parabola with vertex (-1, 2).
You can use the vertical line test on a graph to determine whether a relation is a function. If it is impossible to draw a vertical line that intersects the graph more than once, then each x-value is paired with exactly one y-value. So, the relation is a function.
Given, the function is f(x) = x² + 2x + 3
We have to find the graph of the function.
Let y = x² + 2x + 3
Put x = -3
y = (-3)² + 2(-3) + 3
= 9 - 6 + 3
= 9 - 3
y = 6
Put x = -2
y = (-2)² + 2(-2) + 3
= 4 - 4 + 3
y = 3
Put x = -1
y = (-1)² + 2(-1) + 3
= 1 - 2 + 3
= 4 - 2
y = 2
Put x = 0
y = (0)² + 2(0) + 3
= 0 + 0 + 3
y = 3
Put x = 1
y = (1)² + 2(1) + 3
= 1 + 2 + 3
= 3 + 3
y = 6
We can plot the graph using the points.
The graph of the function f(x) = x² + 2x + 3 is a parabola with vertex (-1, 2).
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if your techer tells you to do questions 38 through 51 in your math book for homework how many questions is that
Answer:
thats 13 questions
Step-by-step explanation:
Answer: 13 questions
Step-by-step explanation: 51-38 equals 13
Jaden goes to dinner with his family. Their total bill comes to $52.25. They received
great service, so they decide to leave a 20% tip. How much should they leave for a
tip?
$16.12
$1.05
$10.45
$2.61
Work Shown:
20% = 20/100 = 0.20
20% of 52.25 = 0.20*52.25 = 10.45
side note: The total cost, including the tip, is 52.25+10.45 = 62.70 dollars
50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.
Negative 2.5 x greater-than-or-equal-to negative 30 is the equivalent expression of 50 minus 2.5 x greater than or equal to 20
How to find an equivalent expression?Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will give you the same value when you simplify
Given: 50 minus 2.5 x greater than or equal to 20
50 - 2.5x ≥ 20
Subtract 50 from both sides:
-2.5x ≥ 20-50
-2.5x ≥ -30
Therefore, the equivalent expression is "negative 2.5 x greater-than-or-equal-to negative 30"
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kerry is going to use these instructions to make a fizzy drink
mix 7 parts apple juice with 3 parts lemonade
kerry thinks that she has 280ml of applejuice and 180 ml lemonade.
if kerry is correct what is the greatest amount of fizzy drink she can make?
second part:
kerry has 280 ml of applejuice but only has 160 ml of lemonade.
Does this affect the greatest amount of fizzy drink she can make?
Give a reason for your answer.
a) She can make 400 milliliters of the fizzy drink.
b) The change does not affect the greatest amount of drink.
If kerry is correct what is the greatest amount of fizzy drink she can make?We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.
If we divide the total amount of apple juice in 7 parts, then each part has:
280ml/7 = 40ml
Then we need 3 parts of 40ml of the lemonade, this is:
3*40ml = 120ml
Then the total amounf of drink fizz that she can make is:
280ml + 120ml = 400ml.
b) Now she has 160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.
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Determine the correct equation for the following verbal sentence:
The ticket price, t, for a concert attended by 220 people equals the total revenue, r, divided by the number of people who attended.
a.
t = StartFraction r Over 220 EndFraction
c.
t = 220r
b.
t = 220 - r
d.
t = 220 + r
Answer:
t =
Given:
The total ticket price =t
Total number of people attended the concert = 350
Total revenue = r
To Find:
The expression for finding the t value
Solution:
The ticket price t =
Substituting the total number of people who attended the concert
t =
Step-by-step explanation:
Hope this helps:)
Question 8(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.
Equations can be categorized as identities or conditional equations.
w = (455.95-155.95)/(37.50)
=300/37.50
=8
So, number of weeks = 8
As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.
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If 12 snickers bars cost $8.40, how much does one bar cost?
Answer:
70¢
Step-by-step explanation:
$8.40/12 bars equals $0.70
Hello everyone, I'm just having trouble on a question for my Calculus work. Does anyone know where to start with this problem? Any help would be greatly appreciated!
Answer:
sin(8w)/1024 -sin(4w)/128 +3w/128
Step-by-step explanation:
No doubt there are a variety of formulas and identities that can be used. Absent knowledge of those, I found it convenient to rewrite the integrand using Euler's formula. It tells you ...
\(\sin(x)=\dfrac{e^{ix}-e^{-ix}}{2i},\quad\cos(x)=\dfrac{e^{ix}+e^{-ix}}{2}\)
After some only slightly messy algebra, we find ...
\(\cos^4(w)\sin^4(w)=\dfrac{\cos(8w)-4\cos(4w)+3}{128}\)
Then the integral becomes straightforward:
\(\displaystyle \int{\cos^4(w)\sin^4(w)}\,dw=\int{\dfrac{\cos(8w)}{128}}\,dw-\int{\dfrac{\cos(4w)}{32}}\,dw+\dfrac{3}{128}\int{}\,dw\\\\=\boxed{\dfrac{\sin(8w)}{1024}-\dfrac{\sin(4w)}{128}+\dfrac{3w}{128}}\)
__
Additional comment
The slightly messy algebra involves the identities ...
(a+b)(a-b) = a² -b²
(a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
This means the given integrand is equivalent to
cos⁴(w) sin⁴(w) = (cos(w) sin(w))⁴ = (1/2 sin(2w))⁴ = 1/16 sin⁴(2w)
Also recall the half-angle identities for sine and cosine:
cos²(x) = 1/2 (1 + cos(2x))
sin²(x) = 1/2 (1 - cos(2x))
Then we can rewrite further as
1/16 sin⁴(2w) = 1/16 (sin²(2w))²
… = 1/16 (1/2 (1 - cos(4w)))²
… = 1/16 (1/4 (1 - 2 cos(4w) + cos²(4w))
… = 1/64 (1 - 2 cos(4w) + 1/2 (1 + cos(8w)))
… = 1/128 (3 - 4 cos(4w) + cos(8w))
You'll end up with the same solution as in the other answer:
\(\displaystyle \int \cos^4(w)\sin^4(w) \, dw = \frac1{128} \int (3 - 4\cos(4w) + \cos(8w)) \, dw \\\\ = \frac{3w-\sin(4w)+\frac18\sin(8w)}{128} + C \\\\ = \boxed{\frac{24w-8\sin(4w)+\sin(8w)}{1024} + C}\)
Natalya designed a patio for her backyard. The two brick
sections will be the same size and concrete fills the rest of
the patio. Her design and the scale she will use to build
the patio are both shown below.
The concrete portion of the patio will cost $3 per square
foot to construct and the brick portion of the patio will
cost $6 per square foot to construct.
How much will Natalya spend constructing the patio with
concrete and brick?
Scale
1 cm = 4 ft.
A
B
6 cm
$432
$648
Brick
Concrete
6 cm
3 cm
Brick
3 cm
OPTIONS
A
$432
B
$648
C
$2,160
D
$3,024
The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.
We are given that;
The concrete portion of the patio cost=$3 per square
To construct and the brick portion of the patio cost= $6 per square
Now,
The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:
6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft
Therefore, the area of the concrete portion is:
24 ft x 12 ft = 288 ft^2
The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:
3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft
Therefore, the area of one brick rectangle is:
12 ft x 24 ft = 288 ft^2
Since there are two brick rectangles, the total area of the brick portion is:
2 x 288 ft^2 = 576 ft^2
Now we can multiply the areas by their costs per square foot to get the costs of each portion:
Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456
The total cost of constructing the patio is the sum of the costs of each portion:
Total cost = $864 + $3456 = $4320
Therefore, by area the answer will be $4320.
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Use the unit circle to find the value of sin (-90)
The value of Sin(90) is equal to 1.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: Sin(90) and to find the value using the unit circle
Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.
The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.
The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.
Hence, Sin (90) is equal to 1.
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I run 3 miles in 20 minutes. What was my average speed in miles per hour?
Consider the equation and the following ordered pairs: (−4,y) and (x,2) . y=−3x−4 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
To satisfy the equation y = -3x - 4, we need to substitute the given values of x and y in the equation and check if it holds true.
For the ordered pair (-4, y):
y = -3(-4) - 4
y = 12 - 4
y = 8
So, the ordered pair (-4, 8) satisfies the equation y = -3x - 4.
For the ordered pair (x, 2):
2 = -3x - 4
6 = -3x
x = -2
So, the ordered pair (-2, 2) satisfies the equation y = -3x - 4.
If \(f(n) = (n - 1)^{2} + 3n\)which statement is true?
To find the statement that is true you need to find each f(n).
\(f(n)=(n-1)^2+3n\)1) f(3)
\(\begin{gathered} f(3)=(3-1)^2+3(3) \\ f(3)=2^2+9 \\ f(3)=13 \end{gathered}\)2) and 3) f(-2)
\(\begin{gathered} f(-2)=(-2-1)^2+3(-2) \\ f(-2)=-3^2-6 \\ f(-2)=3 \end{gathered}\)4) f(-15)
\(\begin{gathered} f(-15)=(-15-1)^2+3(-15) \\ f(-15)=-16^2-45 \\ f(-15)=211 \end{gathered}\)Then, the statemet that is true is 2) f(-2)=3Ryan counts 505,515, 525, 535, 545, 555. By which number does Ryan skip count?
Which of the following is a quadratic equation?
Answer:
x(x-2) = y
Step-by-step explanation:
The highest exponent/power in a quadratic equation is 2. If you multiply x by whatever is in the parenthesis, you'll get a variable with 2 as it's highest exponent/power
Drake makes two transactions today. What can the sum 80 + (-45) mean in terms of Drake's bank
account?
Answer:
Drake's bank account holds
$35
Step-by-step explanation:
What is 80 + (-45) ?
First, Drake puts $80 into his bank account
0+80=80
Then, he withdraws $45 from his bank account
80-45=35
After the two transactions, Drake's bank account holds
$35
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Find the length of FH.
12
11
F
FH
Answer:
23
Step-by-step explanation:
FH=FG+GH
FH=11+12
FH=23
∆ABC is dilated using a scale factor of 12 to produce ∆A'B'C'.
Select all of the statements that apply to the transformation.
m∠A > m∠A' and m∠B > m∠B'
m∠A < m∠A' and m∠B < m∠B'
m∠A = m∠A' and m∠B = m∠B'
area of △ABC < area of △A'B'C'
∆ABC ≅ ∆A'B'C'
∆ABC ~ ∆A'B'C'
Answer:
C, F.
Step-by-step explanation:
All angle measures are preserved in a dilation. And if all angle measures are preserved, it makes the triangles similar by the AA similarity theorem.
Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 5.8-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 4.1% or largest 4.1%.
1. What is the minimum head breadth that will fit the clientele?
2. What is the maximum head breadth that will fit the clientele?
Answer:
1. The minimum head breadth that will fit the clientele is of 4.41-in.
2. The maximum head breadth that will fit the clientele is of 7.19-in.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of 5.8-in and a standard deviation of 0.8-in.
This means that \(\mu = 5.8, \sigma = 0.8\)
1. What is the minimum head breadth that will fit the clientele?
The 4.1st percentile, that is, X when Z has a pvalue of 0.041, so X when Z = -1.74.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.74 = \frac{X - 5.8}{0.8}\)
\(X - 5.8 = -1.74*0.8\)
\(X = 4.41\)
The minimum head breadth that will fit the clientele is of 4.41-in.
2. What is the maximum head breadth that will fit the clientele?
100 - 4.1 = 95.9th percentile, that is, X when Z has a pvalue of 0.959, so X when Z = 1.74.
\(Z = \frac{X - \mu}{\sigma}\)
\(1.74 = \frac{X - 5.8}{0.8}\)
\(X - 5.8 = 1.74*0.8\)
\(X = 7.19\)
The maximum head breadth that will fit the clientele is of 7.19-in.
What is the 100th term in the sequence 15, 22, 29, 36, 43,...
Answer
Step-by-step explanation:
i dont know child
. In a fort, there were provisions for 400 men for 23 weeks. 60 more men joined them. How long will the provisions
last?
The additional 60 men, the provisions will last for approximately 20 weeks.
To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.
Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.
Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.
To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:
Provisions last = Total person-weeks / Number of men
= 9200 / 460
≈ 20 weeks (rounded to the nearest whole number)
The additional 60 men will extend the supply's shelf life to around 20 weeks.
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7. Jose, Tyler and Mike split some money they made working on the weekend. They each worked a different number of hours, so they have to split the money fairly. Jose receives twice the amount that Tyler receives, and Mike receives $10 less than Tyler. Let x represent the amount that Tyler receives. a. Write an expression that represents the total amount that they receive. b. Simplify the expression in part a) by combining like terms.
The expression that represents the total amount that they receive = 2x + x + x-10
The simplification of the expression by Tue combination of the like terms = 4x - 10.
What is simplification?Simplification is defined as the collection of terms that bears the same integer or alphabet so as to arrive at a more simple mathematical expression.
Jose, Tyler and Mike split some money they made working on the weekend as follows;
Jose made a total of = 2x
Tyler made a total of = x
Mike made a total of = x-10
To calculate the total amount of money they all received is to add the whole money each individual received.
That is,
=2x + x + x-10
= 4x -10
The expression that represents the total amount they received = 2x + x + x-10
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Step by step explanation of y-10=9(x+8), written in standard form
Answer:
y-10=9x+72
y-10-72=9x
y-82=9x
y=9x+82
expand and simplify (3x-2) squared
Expanding and simplifying the expression gives:
(3x - 2)² = 9x² - 12x + 4
How to expand the given expression?
Here we want to expand and simplify the expression below:
(3x - 2)²
First let's expand that, we can rewrite this as:
(3x - 2)² = (3x - 2)*(3x - 2)
We can distribute that product to get:
(3x - 2)*(3x - 2) = (3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2)
Now we can keep simplifying this to get:
(3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2) = 9x² - 6x - 6x + 4
9x² - 6x - 6x + 4 = 9x² - 12x + 4
The simplified expression is:
9x² - 12x + 4
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Julie is given two points, (x,y) and (w,z). Which process can she use to find the distance between the points?
One option is to use the distance formula.
In this case, this is what Julie would be working with:
\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(x-w)^2+(y-z)^2}\\\\\)
If Julie knew the values of x, y, w, and z, then she could find a numeric result for the distance (d).
Yeah..I got another one but please hurry :’)
Answer:
6root2
Step-by-step explanation:
3-1,5-1. (2,4)
R=root(4+16). =6root 2
Write and solve an inequality to find the possible values of x.
The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
So, we have
3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
Hence, the inequality tha calculates x is x < 2
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multiply decimals 9.07 × 6.5=
ANSWER
\(58.955\)EXPLANATION
We want to make the given multiplication.
To do this, first, write the numbers as whole numbers:
\(\begin{gathered} 9.07\Rightarrow907\div100 \\ 6.5\Rightarrow65\div10 \end{gathered}\)Now, we have to multiply the two whole numbers and divide the final answer by 1000 (i.e. 100 * 10)
Therefore, we have:
Now, divide by 1000:
\(\begin{gathered} \frac{58955}{1000} \\ \Rightarrow58.955 \end{gathered}\)That is the answer.