Answer:
5x^2 -2x +4
Step-by-step explanation:
(8x^2 + 9) - (3x^2 + 2x + 5)
Distribute the minus sign
(8x^2 + 9) - 3x^2 - 2x - 5
Combine like terms
5x^2 -2x +4
A rectangular chair cushion
measures 4 inches long, 12 inches
wide, and 3 inches high. How many square inches of fabric would you need to cover the cushion
Answer:
144 square inches.
Step-by-step explanation:
4*12*3=144
what is the range of the function f(x)=(x+4)²+5
Answer:
[tex]Range=\left \{y|y\geq 5\right \}[/tex]
Step-by-step explanation:
Since given the expression, this represents graphically a parabola with arms pointing up, and a vertical translation of its vertex 5 units up, then the range of the function must be all the y values such that they are greater or equal to 5. This is written as:
[tex]Range=\left \{y|y\geq 5\right \}[/tex]
help pls :(((( i don’t get this
Answer:
[tex]\large \boxed{\mathrm{B}}[/tex]
Step-by-step explanation:
3 1/2 is also 0+3 1/2
Arrow from 0 goes to 3 1/2.
3 1/2 - 6 = -2 1/2
Arrow from 3 1/2 goes to -2 1/2.
It is known that 60% of customers will need additional maintenance on their vehicle when coming in for an oil change. A random sample of 48 customers is taken. What is the probability that more than 70% of customers in the sample will need additional maintenance
Answer:
the probability that more than 70% of customers in the sample will need additional maintenance is 0.0371
Step-by-step explanation:
From the information given:
we are to determine the probability that more than 70% of customers in the sample will need additional maintenance
In order to achieve that, let X be the random variable that follows a binomial distribution.
Then X [tex]\sim[/tex] Bin(48, 0.6)
However 70% of 48 samples is
= 0.7 × 48 = 33.6 [tex]\simeq[/tex] 34
Therefore, the required probability is:
= P(X> 34)
[tex]= \sum \limits ^{48}_{x=34} (^{48}_{x}) (0.6)^x(1 - 0.6)^{48-x}[/tex]
[tex]= \dfrac{48!}{34!(48-34)!} (0.6)^{34} (0.4)^{48-34}[/tex]
[tex]= 4.823206232 \times 10^{11} (0.60)^{34}(0.4)^{14}[/tex]
= 0.03709524328
[tex]\simeq[/tex] 0.0371
What is nine more than a number y, if that number is 4?
Answer:
13
Step-by-step explanation:
if y = 4, then 4 + 9 = 13
Answer:
[tex]\huge\boxed{13}[/tex]
Step-by-step explanation:
The given condition is:
=> y + 9
Given that y = 4
=> 4 + 9
=> 13
the remains of an ancient ball court include a rectangular playing alley with a perimeter of about 64 M. the length of the alley is 2 times the width. find the length and the width of the playing alley
Answer:
[tex]Length = \frac{64}{3}m[/tex]
[tex]Width= \frac{32}{3}m[/tex]
Step-by-step explanation:
Given
[tex]Perimeter = 64m[/tex]
[tex]Length = 2 * Width[/tex]
Required
Determine the length and the width
Since the alley is rectangular, the perimeter is as follows;
[tex]Perimeter = 2 (Length * Width)[/tex]
Substitute 64m for Perimeter
[tex]64m = 2(Length + Width)[/tex]
Substitute 2 * Width for Length
[tex]64m = 2(Width+ 2 * Width)[/tex]
[tex]64m = 2(Width+ 2 Width)[/tex]
[tex]64m = 2(3 Width)[/tex]
[tex]64m = 6Width[/tex]
Divide both sides by 6
[tex]Width= \frac{64m}{6}[/tex]
[tex]Width= \frac{32}{3}m[/tex]
Recall that
[tex]Length = 2 * Width[/tex]
[tex]Length = 2 * \frac{32}{3}m[/tex]
[tex]Length = \frac{64}{3}m[/tex]
Triangle XYZ is dilated by a factor of 3 with the center of dilation at the origin to form triangle X′Y′Z′. What are the coordinates of triangle X′Y′Z′? Question 15 options:
A) X′ (0, 9), Y′ (0, 0), Z′ (15, 0)
B) X′ (0, 6), Y′ (0, 0), Z′ (10, 0)
C) X′ (0, 15), Y′, (0, 0), Z′ (5, 0)
D) X′ (0, 6), Y′ (0, 0), Z′ (15, 0)
Answer:
D) X′ (0, 6), Y′ (0, 0), Z′ (15, 0)
Step-by-step explanation:
From the image attached, given that the location of the triangle is at:
X(0, 2). Y(0, 0), Z(5, 0)
Transformation is the movement of a point from its initial position to a new position. A shape is transformed by transforming all the points in the shape. Types of transformations are reflection, rotation, dilation and translation.
A dilation produces the same shape but different size. If the dilation < 1, then it is a reduction but if dilation > 0 then it is an enlargement.
A point A(x, y) which is dilated by a factor of c at the origin has new coordinates at A'(cx, cy).
Since triangle XYZ is dilated by a factor of 3 with the center of dilation at the origin, this represents an enlargement and the new coordinates of the triangle are:
X'(3*0, 3*2) = X'(0, 6)
Y'(3*0, 3*0) = Y'(0, 0)
Z'(3*5, 3*0) = X'(15, 0)
Answer:
D
Step-by-step explanation:
What is the slope of the line below?
(-4,6)
(1, -9)
Answer:
-3
Step-by-step explanation:
Slope = [tex]\frac{y_{2} -y_{1}}{x_{2} - x_{1} }[/tex]
slope = 6 - -9/ -4 - 1
slope = 15 / -5
slope = -3
Modeling Real-World Problems with Composite Functions
A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Of(x) = 0.35x represents the diseount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fog)(x) = 0.35(0.07x) = 0.0245x.
Of(x) = 0.65x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fºg)(x) = 0.65(0.07x) = 0.0455x.
Of(x) = 1.07x represents the price after taxes and g(x) = 0.65x represents the discount price. The total price would
be (fºg)(x) = 1.07(0.65x)= 0.6955x
O f(x) = 1.07x represents the price after taxes and g(x) = 0.35x represents the discount price. The total price would
be (fog)(x) = 0.35(1.07x)=0.3745x.
Answer:
The third option: (f°g)(x)=1.07(0.65x)=06955x
Step-by-step explanation:
The reason I chose this is because 0.65x is the discount price. That's because 35% off is the same as 1.00-0.35 which equals 0.65. After that you would multiply that discount price by 1.07 because you want the 7% sales tax added on to the discount price. Therefore, I would choose the third option as my answer.
Compare 8 • 10^7 to 2 • 10^4 (how many times larger)
Answer:
I believe the answer is 4,000 times larger.
Step-by-step explanation:
8*10⁷ = 80000000
2*10⁴ = 20000
20000*4000 = 80000000
Write as a radical expression and evaluate if possible. 8 1/3
Answer:
[tex]\huge \boxed{2}[/tex]
Step-by-step explanation:
[tex]8^\frac{1}{3}[/tex]
Apply rule : [tex]a^\frac{1}{3}=\sqrt[3]{a}[/tex]
[tex]8^\frac{1}{3}=\sqrt[3]{8}[/tex]
8 is a perfect cube. Evaluate the cube root of 8.
[tex]\sqrt[3]{8}=2[/tex]
Answer:
Radical expression
[tex] \sqrt[3]{2} [/tex]
Evaluation
[tex] {8}^{ \frac{1}{3} } = 2[/tex]
Step-by-step explanation:
8^(⅓) = ³√8
=³√(2×2×2)
=³√(2³)
= 2
BRAINLIEST PLEASE
In the number 3355 how many times greater is the 3 on the left than the 3 on the right
Answer:
9 times
Step-by-step explanation:
Given
[tex]Number = 3355[/tex]
Required
Determine how many times, the 3 on the left is greater than that on the right
[tex]Number = 3355[/tex]
First, we need to determine the value of the three on the left
To get its value, we have to change all other digits to 0. This gives
[tex]Left\ 3 = 3000[/tex]
Next, we need to determine the value of the three on the righy
Similarly, we have to change all other digits to 0. This gives
[tex]Right\ 3 = 0300[/tex]
[tex]Right\ 3 = 300[/tex]
Next, we calculate the positive difference between these two values and divide by the value of the Right 3
[tex]Result = \frac{Left\ 3 - Right\ 3}{Right\ 3}[/tex]
[tex]Result= \frac{3000 - 300}{300}[/tex]
[tex]Result= \frac{2700}{300}[/tex]
[tex]Result = 9[/tex]
Hence, the left 3 is 9 times greater than the right 3
Suppose Kaitlin places $ 4000 in an account that pays 18% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
sa
(b) Find the amount in the account at the end of 2 years.
Answer:
a) $4720
b) $5569.60
Step-by-step explanation:
Initial amount = $4000
Interest rate = 18% PA compounded
Amount after 1 year
$4000*1.18 = $4720Amount after 2 years
$4720*1.18 = $5569.60PLEASE HELP ASAP!!!!!!!!!!!!!!!!!
Answer:
Twelve tickets cost $30 --> True
Thirty tickets cost $12 --> False
Each additional costs $2.50 --> True
The table is a partial rep --> True
ordered pairs --> False
Step-by-step explanation:
Twelve tickets cost $30 --> True, you can literally see that in the table
Thirty tickets cost $12 --> False, 30 is not in the table so you don't have that information. Besides, $12 is an unlikely low value for so many tickets.
Each additional costs $2.50 --> True, you can see the difference in the TotalCost column to be consistently 2.50.
The table is a partial rep --> True, values below 11 are not shown for example.
ordered pairs --> False --> Then the x value should be first, e.g., (11, 27.50), since the cost y is a function of the number x.
the product of x and the sum of 6 and 8 times the square of x
Answer:
x(6 + 8x²) or 6x + 8x³.
Step-by-step explanation:
"The square of x" can be represented by x² and 8 times that would be 8 * x² or 8x². The sum of 6 and 8x² can be represented by 6 + x² and the product of x and 6 + x² can be represented by x * (6 + 8x²) or x(6 + 8x²) which simplifies to 6x + 8x³.
Answer:
14x * x^2
Step-by-step explanation:
So you just have to read very carefully on these questions.
the product of x and the sum of 6 and 8
x times 6+8= x times 14= 14x
Product= multiply
Sum= add
that answer times the square of x
x^2
=14x times x^2
How would you read the number 7,256.85?
Answer:
seven-thousand two-hundred and fifty-six point eighty-five
Step-by-step explanation:
7 in the thousands place, two in the hundredths 5 in the tenths and 6 in the ones
The number 7,256.85 is read as Seven thousand two hundred fifty six point eight five.
Here,
The number is 7,256.85.
We have to find how to read this number.
What is place value?
Place value is the value represented by a digit in a number on the basis of its position in the number.
Now,
The number is 7,256.85.
In words it can be written as,
7,256.85 = Seven thousand two hundred fifty six point eight five.
So, The number 7,256.85 is read as Seven thousand two hundred fifty six point eight five.
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A random sample of 1700 workers in a particular city found 578 workers who had full health insurance coverage. Find a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage.
Answer: (31.75%, 36.25%)
Step-by-step explanation:
Let p be the proportion of workers in this city who have full health insurance coverage.
As per given,
Sample size : n= 170
Number of workers who had full health insurance coverage.=578
i.e. sample proportion: [tex]\hat{p}=\dfrac{578}{1700}\approx0.34[/tex]
Also, z-score for 95% confidence level : 1.96
Formula to find the confidence interval for p :
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]0.34\pm (1.96)\sqrt{\dfrac{0.34(1-0.34)}{1700}}[/tex]
[tex]=0.34\pm (1.96)\sqrt{0.000132}\\\\=0.34\pm (1.96)(0.011489125)\\\\\approx 0.34\pm0.0225\\\\=(0.34-0.0225,\ 0.34+0.0225)\\\\=(0.3175,\ 0.3625) =(31.75\%,\ 36.25\%)[/tex]
Hence, a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage= (31.75%, 36.25%)
The yearly attendance at a local movie theater is 82,000 and grows continuously at a rate of 5.1% each year. What is the approximate attendance at the movie theater in ten years? (3 points) a 136,554 b 85,552 c 134,847 d 123,820
Answer:
c. 134,847
Step-by-step explanation:
82,000 x (1.051)^10 = 82,000 x 1.64447456 = 134,847
The rate of change in revenue for Under Armour from 2004 through 2009 can be modeled by dR /dt = 13.897t + 284.653 t where R is the revenue (in millions of dollars) and t is the time (in years), with t = 4 corresponding to 2004. In 2008, the revenue for Under Armour was $725.2 million.
†
(a) Find a model for the revenue of Under Armour. (Round your constant term to two decimal places.) R(t) = 6.9485t2+284.653 ln(t)-311.42 Correct: Your answer is correct.
(b) Find Under Armour's revenue in 2009. (Round your answer to two decimal places.) $ million
Answer:
The revenue is [tex]R(9) = \$ 876.9[/tex]
Step-by-step explanation:
From the question we are told that
The rate of change in revenue for Under Armour from 2004 through 2009 is
[tex]\frac{d R }{dt } = 13.897t + \frac{284.653}{t}[/tex]
Now
[tex]dR = (13.897t + \frac{284.653}{t})dt[/tex]
Integrating both sides to obtain R(t)
[tex]\int\limits dR = \int\limits (13.897t + \frac{284.653}{t})dt[/tex]
[tex]\int\limits dR = \int\limits (13.897\frac{t^2}{2} + 284.653(ln (t)) ) + C[/tex]
=> [tex]R(t) = 6.9485t^2 + 284.653(ln (t) ) + C[/tex]
From the question we have that at t = 8 [tex]R(8)= \$ 725.2 \ million[/tex]
[tex]725.2 = 6.9485(8)^2 + 284.653(ln (8) ) + C[/tex]
=> [tex]C = -311.4[/tex]
So
[tex]R(t) = 6.9485t^2 + 284.653(ln (t) ) -311.4[/tex]
At t = 9
[tex]R(9) = 6.9485*(9)^2 + 284.653(ln (9) ) -311.4[/tex]
[tex]R(9) = \$ 876.9[/tex]
Simplify to create an equivalent expression 11/12-1/6q+5/6q-1/3
Answer: 7/12 + 2/3q
Step-by-step explanation:
[tex]\frac{11}{12} - \frac{1}{6}q + \frac{5}{6}q - \frac{1}{3}[/tex] Combine like terms subtract 1/3 from 11/12 and add -1/6q and 5/6q.
[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]
[tex]-\frac{1}{6}q + \frac{5}{6} q = \frac{4}{6}[/tex]q = 2/3 q
last month you had an outstanding check of $87.90 that had not yet been cashed, so it did not show up on your statement. This month, you wrote checks totaling $379.42. You made one deposit of $100, and you withdrew $60 from an ATM. If the check from last month was cashed and recorded on your statement, and if the bank paid $0.23 in interest, then by how much did your account balance change this month?
500.99
add it alll up and leave the 87.90 for last
Answer:
Step-by-step explanation:
decreased by $427.09
Math-Limits and Derivative. Could anybody help me,please ?
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]\displaystyle f'(0)=\lim_{x\rightarrow0} {\dfrac{f(x)-f(0)}{x-0}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1}{x}-k}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1-kx}{x}}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\sqrt{1+x}-1-kx}{x^2}}\\[/tex]
Thank you
Identify the problem with the following study. An internet poll on a website asks people to indicate whether or not they have a cable TV subscription. 1974 people respond with 847 indicating that they do have a cable TV subscription.
A.nonresponse
B.voluntary response
C.precise numbers
D.correlation and causality
Answer:
B. VOLUNTARY RESPONSE
Step-by-step explanation:
The sampling method here is voluntary response.
What are Sampling Methods?Sampling methods are used to choose members from the population to be a part of a study.
There are different kinds of sampling methods used in different scenarios like simple random sample, stratified random sample, systematic random sample and cluster random sample.
There are also methods like voluntary response and convenience sample which are not that effective.
Voluntary response sample is a method of sampling by which researcher requests to members of a population to take part in the sample and the member decides to whether join or not to join in the sample.
Given study is an internet poll where the researches asks people to indicate whether or not they have a cable subscription. 1974 people responded to the poll fully on their consent.
Researcher has not selected or did any systematic method in selecting these members.
Hence the sampling study given here worked through voluntary response sampling.
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Martha went to the store with$75.00 she bought 3 pairs of socks for $4.00 each she bought 2 shirts for $20.00 each and she bought a skirt for $21.00 how much money did she have left?
Answer:
$2 dollers
Step-by-step explanation:
2. Solve for z and express your answer in interval notation: 10 – 4z < 20
Answer:
z > -5/2
Step-by-step explanation:
Since both sides are divided by a negative number, the equality is switched.
10 - 4z < 20
(10 - 4z) - 10 < 20 - 10
-4z < 10
(-4z)/-4 < 10/-4
z > -5/2
The solution for z will be;
⇒ z ∈ (- 2.5 , ∞ )
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 10 - 4z < 20
Now,
Since, The inequality is,
⇒ 10 - 4z < 20
Solve for z as;
⇒ 10 - 4z < 20
⇒ 10 - 4z + 4z < 20 + 4z
⇒ 10 < 20 + 4z
⇒ 10 - 20 < 4z
⇒ - 10 < 4z
⇒ - 2.5 < z
⇒ z ∈ (- 2.5 , ∞ )
Thus, The interval notation is,
⇒ z ∈ (- 2.5 , ∞ )
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Help me please ❤️❤️❤️
Answer:
Hey there!
Point U has coordinates of (-5, 4)
Let me know if this helps :)
Answer:
(-5,4) is the coordinate of point U
What is the length of CD to the nearest 10th?
Answer:
[tex]\huge \boxed{\mathrm{10.3 \ units}}[/tex]
Step-by-step explanation:
To solve for CD, we can create a right triangle.
Where CD becomes the hypotenuse.
The length of the base of the triangle is 9 units.
The length of the height of the triangle is 5 units.
Apply Pythagorean theorem to solve for the hypotenuse.
[tex]\sf hypotenuse = \sqrt{(base )^2 +(height )^2 }[/tex]
[tex]c=\sqrt{9^2 +5^2 }[/tex]
[tex]c=\sqrt{106}[/tex]
[tex]c \approx 10.29[/tex]
How do I evaluate this? there’s a picture.
Answer:
it is 3/3
Step-by-step explanation:
2 tan is 2/3 +cos is 1/4 +2/4
Points F (0,0), G (9,0), and H (9,12) are the vertices of a triangle.
What is the distance from point F to point H?
A. 9
B. 12
C. 15
D. 21
Answer:
15
Step-by-step explanation:
Because I said so
The distance from point F to point H is 15 units. Option C is correct.
In order to get the distance from point F to point H, we will use the distance formula as shown:
[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given the coordinate points F(0,0) and H(9, 12)
[tex]FH=\sqrt{(12-0)^2+(9-0)^2}\\FH =\sqrt{12^2+9^2}\\FH=\sqrt{144+81}\\FH=\sqrt{225}\\FH = 15units[/tex]
Hence the distance from point F to point H is 15 units. Option C is correct.
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What is the value of x in the equation 2x + 1/2x + 2(1+x) = 29?
Answer:
x = 6Step-by-step explanation:
[tex]2x + \frac{1}{2} x + 2(1 + x) = 29[/tex]
Multiply through by 2
That's
[tex]4x + x + 4(1 + x) = 58[/tex]
Expand
That's
5x + 4 + 4x = 58
9x = 58 - 4
9x = 54
Divide both sides by 9
That's
[tex] \frac{9x}{9} = \frac{54}{9} [/tex]
We have the final answer as
x = 6Hope this helps you