Answer: A) 21.25 ≤ x ≤ 22.75
Step-by-step explanation:
Given, Average weight of basketballs = 22 ounces
It is possible for its weight to vary at most 0.75 ounces from this average.
Let x denotes the weight of the basket ball.
Then, the required range for a basketball's weight:
Average-0.75 ≤ x ≤ Average+0.75
⇒22-0.75 ≤ x ≤ 22+0.75
⇒21.25 ≤ x ≤ 22.75
Hence, the range for a basketball's weight: 21.25 ≤ x ≤ 22.75 .
Correct option: A) 21.25 ≤ x ≤ 22.75
Solve for p. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. -31p+79 > -59p+81
Answer:
The answer is
p > 1/14Step-by-step explanation:
-31p+79 > -59p+81
Group like terms
Send the constants to the right side of the expression and those with variables to the left side
That's
- 31p + 59p > 81 - 79
Simplify
We have
28p > 2
Divide both sides by 28
We have the final answer as
p > 1/14Hope this helps you
Assume that the random variable X is normally distributed, with mean p = 100 and standard deviation o = 15. Compute the
probability P(X > 112).
Answer:
P(X > 112) = 0.21186.
Step-by-step explanation:
We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.
Let X = a random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 100
[tex]\sigma[/tex] = standard deviaton = 15
Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)
P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)
= 1 - 0.78814 = 0.21186
The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.
Please answer this question now
Answer:
e =7.1
Step-by-step explanation:
[tex]Hypotenuse = 10\\Opposite =e\\Adjacent =7\\\\Using\:Pythagoras\:Theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\10^2 =e^2 + 7^2\\100 =e^2+49\\100-49=e^2\\\\51 =e^2\\\sqrt{51} =\sqrt{e^2}\\ e = 7.141\\\\e = 7.1[/tex]
Which is the best description of the equivalency of the two expressions? Expression 1 Expression 2 5 x squared minus 2 x minus 4 + 6 x + 3 6 x squared minus 6 x + 6 minus x squared + 10 x minus 7 The two expressions are not equivalent because when x = 2, the two expressions do not have the same value. The two expressions are not equivalent because when they are simplified, they do not have the same coefficients for the x squared and x terms. They are equivalent because the sum of the constants is the same in both expressions. They are equivalent because when x = 2, the two expressions have the same value.
Answer:
The correct option is (D).
Step-by-step explanation:
The two expressions are:
[tex]\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7[/tex]
On simplifying both the expressions we get:
[tex]\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1[/tex]
Compute the value of both expressions for x = 2 as follows:
[tex]\text{Exp}_{1}=5(2)^{2}+4(2)-1=27\\\\\text{Exp}_{2}=5(2)^{2}+4(2)-1=27[/tex]
The value of both expressions are same for x = 2.
Thus, the correct option is:
"They are equivalent because when x = 2, the two expressions have the same value."
Answer:
d
Step-by-step explanation:
The graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k: a parabola with the vertex 4, 1 What is the value of k?
Answer:
k = 1
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (4, 1 ), thus k = 1
What is the answer to 85% of 62
Answer:
52.7
Step-by-step explanation:
Of means multiply
85% * 62
.85 * 62
52.7
Turn the percentage into a decimal.
85% = 0.85
Multiply.
62 * 0.85 = 52.7
So, 52.7 is 85% of 62.
Best of Luck!
Please helpppp!!!
Solve: x^2 - 4x-5=0
Answer:
[tex]x=-1,5[/tex]
Step-by-step explanation:
[tex]x^2-4x-5=0[/tex]
In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.
To factor, find two numbers that when multiplied equal a(c) and when added equal b.
a=1, b=-4, and c=-5.
So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.
-5 and 1 are the possible numbers. Therefore:
[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]
find the value of b here
Answer:
Step-by-step explanation:
We will start with the angle that measures 57 degrees. This angle is supplementary to the one next to it coming off the straight line. 180 - 57 = 123.
The rule for quadrilaterals is that same side angles are supplementary, so the angle next to the 123-degree angle (to the immediate left of that angle 123) is 57. THAT 57-degree angle is supplementary to angle b, so angle b = 180 - 57 which is 123. So C is your answer.
Answer:
do you think you can send me the work for the program
Step-by-step explanation:
i got 1 day left and im not close to finishing it please help me out please respond with any way to contact you thanks
how many cups in 34 gallons
Answer:
544 cups
Step-by-step explanation:
1 gallon consists of about 16.0047 cups, 34x16 is 544
X*2+1=10 then x=? Tell me the value of x
Answer:
4.5Step-by-step explanation:
[tex]x \times 2 + 1 = 10[/tex]
[tex]2x + 1 = 10[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 10 - 1[/tex]
Subtract the numbers
[tex]2x = 9[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Calculate
[tex]x = 4.5[/tex]
Hope this helps..
Best regards!!
3 ( 1 - 20 ) + 10 = 4
Answer:
3(1 - 20) + 10 = 4
3 * (-19) + 10 = 4
-57 + 10 = 4
-47 = 4
Since the two are not equal, this statement is false/invalid.
Hope this helps!
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides
of this triangle?
O 5cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
Choice D - 8cm and 9cm.
Step-by-step explanation:
The other sides are not greater than 13.
A: 5 + 8 = 13
B: 6 + 7 = 13
C: 7 + 2 = 9
However, D is greater than 13 and is the correct answer.
D: 8 + 8 = 16.
Option d: 8 cm and 9 cm.
There is a theorem in mathematics stating:
" The sum of length of two sides of any triangle is greater than the rest third side"
According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.
The 4th option has 8 cm and 9 cm for which we have:
8 + 9 > 13
Thus this option follows the theorem.
Hence fourth option is correct.
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A number is 30% of 20% of the number x.
Answer:
6/100x
Step-by-step explanation:
Answer:6/100x
Step-by-step explanation:
In a recent year 5 out of 6 movies cost between $50 and $99 million to make. At this rate, how many movies in a year with 687 new releases would you predict to cost between $50 and $99 million to make
Answer:
573 movies
Step-by-step explanation:
Here, we have 5 out of 6 movies having that cost
Therefore the rate we will be working with is 5/6
Now there are 687 new releases, the value that cost the given price range will be; 5/6 * 687 = 572.5 which is approximately 573
im not sure wether to replace the minus signs with addition, so if you could help me that would be nice :) 1.2y+4.5-3.4y-6.3
Answer:
-2.2y - 1.8
Step-by-step explanation:
We are to simplify the expression:
1.2y + 4.5 - 3.4y - 6.3
Collect like terms:
1.2y - 3.4y + 4.5 - 6.3
Simplify:
-2.2y - 1.8
That is the answer.
An actor invests some money at 8% simple interest, and $21 comma 000 more than four times the amount at 10% simple interest. The total annual interest earned from the investment is $49 comma 140. How much did he invest at each amount? Use the six-step method.
Answer:
First investment = $98000
Second = $413,000
Step-by-step explanation:
Given the following :
Investment 1:
Let first investment = f
Rate = 8% = 0.08
Investment 2:
$21,000 more than 4 times of investment 1:
4f + 21000
Rate = 10% = 0.1
Total annual interest earned from both :
$49,140
Interest on investment 1 + interest on investment 2 = $49,140
To solve:
Simple Interest = principal * rate * time
Time = 1 year
Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)
49140 = 0.08f + 0.4f + 2100
0.48f = 47040
f = 47040 / 0.48
f = 98000 = first investment
Second investment :
4f + 21000
= 4(98000) + 21000
= $413,000
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 900 and 975 hours.
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:
standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]
standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%
Answer:
2.35 babyyyyyyyyyyy
Step-by-step explanation:
Acellus sux
Consider the y-intercepts of the functions:
f(x) = |x – 1] + 2
g(x) =
(x + 3)
h(x) = (x + 1) -3
1
What is the ordered pair location of the greatest y-intercept of the three functions?
Answer:
+3, 0
Step-by-step explanation:
y-intercept for f(x) is when x = 0, so it is +1, 0
y-intercept for g(x) is when x = 0, so it is +3, 0
y-intercept for h(x) is when x = 0, so it is -2, 0
The y-intercept of a function is the point where x = 0.
The ordered pair that represents the greatest y-intercept is (0,3)
The functions are given as:
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Set x = 0, and solve the functions
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
Substitute 0 for x
[tex]\mathbf{f(0) = |0 - 1| + 2}[/tex]
[tex]\mathbf{f(0) = |- 1| + 2}[/tex]
Remove absolute brackets
[tex]\mathbf{f(0) = 1 + 2}[/tex]
[tex]\mathbf{f(0) = 3}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
Substitute 0 for x
[tex]\mathbf{g(0) = (0 + 3)}[/tex]
[tex]\mathbf{g(0) = 3}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Substitute 0 for x
[tex]\mathbf{h(0) = (0 + 1) - 3}[/tex]
[tex]\mathbf{h(0) = 1 - 3}[/tex]
[tex]\mathbf{h(0) = - 2}[/tex]
Hence, the ordered pair that represents the greatest y-intercept is (0,3)
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Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
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What is the circumference of a circle with a diameter of 100m. A 100m B 157m C 300 m D 314m
Answer:
C = 314 m
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
Using 3.14 for pi
C = 3.14 * 100
C = 314 m
Answer:
The answer is option D.
314mStep-by-step explanation:
Circumference of a circle = πd
Where d is the diameter
From the question
d = 100m
Circumference of the circle is
100π
= 314.2
Which is 314m to the nearest whole number
Hope this helps you
How can 2182 be written as the sum of four consecutive whole numbers?
Answer:
544 + 545 + 546 + 547
explanation: if the numbers are consecutive whole numbers then it would be near the ¼ of the given number
Factorize: 14x^6-45x^3y^3-14y^6
Answer:
(7x^3+2y^3)(2x^3−7y^3)
A, B, and C are midpoints of ∆XYZ. What is the length of ? YZ
Answer:
[tex]YZ = 48[/tex]
Step-by-step explanation:
Given
[tex]AB = 24[/tex]
[tex]XZ = 60[/tex]
Required
Find YZ
From the attachment, AB is parallel and equal to YC;
This implies that
[tex]AB = YC = 24[/tex]
Given that C is the midpoint of YZ;
This implies that
[tex]YC = CZ = 24[/tex] and [tex]YZ = YC + CZ[/tex]
Substitute values for YC and CZ
[tex]YZ = 24 + 24[/tex]
[tex]YZ = 48[/tex]
Answer:
48
Step-by-step explanation:
A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π .
Answer:
12π inches
Step-by-step explanation:
s = rθ
s = (21) (4π/7)
s = 12π
The length of the arc will be;
⇒ Arc = 37.68 inches
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The central angle = 4π/7
And, A circle has a radius of 21 inches.
Now,
We know that in circle;
⇒ Arc = Radius × Angle
Substitute all the values, we get;
⇒ Arc = 21 × 4π/7
⇒ Arc = 3 × 4 × 3.14
⇒ Arc = 37.68 inches
Thus, The length of the arc will be;
⇒ Arc = 37.68 inches
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The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options. $8 $9 $11 $13 $14
Answer:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8 . YES
$9 . HELL NO
$11 . DEFINITLY NOT
$13 . GET OUTTA HERE
$14 . MMM YES
Step-by-step explanation:
Answer:
A and E or 8, 14
Step-by-step explanation:
Please answer this in two minutes
Answer:
u = [tex]\sqrt{6}[/tex].
Step-by-step explanation:
This is a 45-45-90 triangle.
That means that there are two side lengths with lengths of x, and a hypotenuse with a length of xsqrt(2). We can then set up a proportion.
[tex]\frac{1}{\sqrt{3} } =\frac{\sqrt{2} }{u}[/tex]
1 * u = [tex]\sqrt{3} * \sqrt{2}[/tex]
u = [tex]\sqrt{6}[/tex].
Hope this helps!
The cost of importing five dozen china dinner sets, billed at $32 per set, and paying a duty of 40%, is
Answer:
duty = 64
Total cost is 224
Step-by-step explanation:
First find the cost of the 5 sets
5 * 32 = 160
Then find the duty
160 * 40%
160 * .4 = 64
Add this to the cost of the sets
160+64 =224
What is the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color?
You would assume that in this figure, the number of colored sections with which are not colored with respect to a " touching " colored section, would be half of the total colored sections. However that is not the case, the sections are not alternating as they still meet at a common point. After all, it notes no two touching sections, not adjacent sections. Their is no equation to calculate this requirement with respect to the total number of sections.
Let's say that we take one triangle as the starting. This triangle will be the start of a chain of other triangles that have no two touching sections, specifically 7 triangles. If a square were to be this starting shape, there are 5 shapes that have no touching sections, 3 being a square, the other two triangles. This is presumably a lower value as a square occupies two times as much space, but it also depends on the positioning. Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.
Respectively the solution for this second figure is 5 sections as well.
a man buys a dozen cameras for $1800.He sells them at a profit of $36 each.Express his profit as a percentage of his selling price.
Step-by-step explanation:
The solution is the document i sent please check through.
The net of a solid is shown below:
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square.
What is the surface area of the solid?
18 square inches
27 square inches
36 square inches
45 square inches
Answer:
The answer is 45 inches².
Step-by-step explanation:
First, you have to find the area of each triangle:
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 3 \\ let \: height = 6[/tex]
[tex]area = \frac{1}{2} \times 3 \times 6[/tex]
[tex]area = \frac{1}{2} \times 18[/tex]
[tex]area = 9 \: \: {inches}^{2} [/tex]
Assuming that the formula for surface area of pyramid is Surface area = base area(area of square) × 4(area of triangle):
[tex]base \: area = 3 \times 3 = 9[/tex]
[tex]area \: of \: triangle = 9[/tex]
[tex]s.a = 9 + 4(9)[/tex]
[tex]s.a = 9 + 36[/tex]
[tex]s.a = 45 \: \: {inches}^{2} [/tex]