Answer:
3.04
Step-by-step explanation:
Given the prediction equation:
y_hat = 145.5 -5.5*x
- - - - x - - - - - - - - - у
1 - - 10.36 - - - - 87.87
2 - - 9.96 - - - - 89.83
3 - - 12.50 - - - - 71.61
1) y_hat = 145.5 -5.5*(10.36)
y_hat = 145.5 - 56.98 = 88.58
2) y_hat = 145.5 -5.5*(9.96)
y_hat = 145.5 - 54.78 = 90.72
3) y_hat = 145.5 -5.5*(12.50)
y_hat = 145.5 - 68.75 = 76.75
Root mean squared error (RMSE) :
Number of observations (n) = 3
√(Σ(y_hat - y)^2) / n
y_hat = predicted value
y = actual value
Σ[(88.58-87.87)^2+(90.72-89.83)^2+(76.75-71.61)]
Σ(0.71^2) + (0.89^2) + (5.14^2)
27.7158 / 3 = 9.2386
√9.2386
= 3.0395065
= 3.04
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 = $5569.60the 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
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]
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
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.
Learn more here: https://brainly.com/question/22624745
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]
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It is believed that the machine is underfilling the bags. A 27 bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is no sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
We are given;
n = 27 bags
Sample mean;X = 402 gram
Population mean;μ = 404 gram
Variance = 676
We know that, standard deviation(σ) = √variance
Thus;
σ = √676
σ = 26
The hypotheses are;
Null hypothesis; H0: μ = 404
Alternative hypothesis; HA: μ < 404
Let's find the z-score from the formula;
z = (X - μ)/(√σ/n)
z = (402 - 404)/√(26/27)
z = -2.04
From the z-distribution table attached, we have a p-value of 0.02068
This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled
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.
Learn more about the place value visit:
https://brainly.com/question/23732536
#SPJ2
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:
PLEASE 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.
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 , ∞ )
Learn more about the inequality visit:
https://brainly.com/question/25275758
#SPJ2
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.
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%)
A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30 After what number of hours will the amount of candy produced be the same for both machines?
Answer:
In 4 hours.
Step-by-step explanation:
Just equate f(x) = g(x). So:
15x + 90 = 30x + 30
60 = 15x
x = 4 hours.
In 4 hours the amount of candy produced be the same for both machines.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30.
The value of time will be calculated below:-
Just equate f(x) = g(x).
15x + 90 = 30x + 30
60 = 15x
x = 4 hours.
Therefore, In 4 hours the amount of candy produced is the same for both machines.
To know more about expression follow
https://brainly.com/question/723406
#SPJ2
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
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
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
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
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
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]
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
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.
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
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
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
PLEASE HELP !!! The height of a rectangle is twice the width and the area is 32. Find the dimensions.
Answer:
The rectangle has a width of 4 and a height of 8
Step-by-step explanation:
Let the height of the rectangle be H and the width be W.
We know the height of the rectangle is twice the width, so:
H = 2W
The area of a rectangle, A, is given by A = W * H, so in this case:
32 = W * 2W
32 = 2W²
W² = 16
W = 4
Knowing that the width is 4, the height must be 8. This gives us an area of 32.
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
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
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
Solve each absolute value equation and match them with the correct solution.
Answer:
Step-by-step explanation:
First we must understand that absolute value of a function returns both positive and negative function.
1) Given |x-6| = 5
For the positive value of the function:
x-6 = 5
Add 6 to both sides
x-6+6 = 5+6
x = 11
For the negative function:
-(x-6) = 5
Open the parentheses
-x+6 = 5
Subtract 6 from both sides
-x+6-6 = 5-6
-x = -1
x = 1
Hence x = 1, x = 11
2 ) Given |3x-7| = 12
For the positive value of the function:
3x-7 = 12
Add 7 to both sides
3x-7+7 = 12+7
3x = 19
x = 19/3
For the negative function:
-(3x-7) = 12
Open the parentheses
-3x+7 = 12
Subtract 7 from both sides
-3x+7-7 = 12-7
-3x = 5
x = -5/3
Hence x = 19/3, x = -5/3
3) Given |2x+9| - 10= 5
For the positive value of the function:
2x+9-10= 5
2x-1 = 5
Add 1 to both sides
2x-1+1 = 5+1
2x = 6
x= 3
For the negative function:
-(2x+9)-10 = 5
Open the parentheses
-2x-9-10 = 5
-2x-19 = 5
Add 19 to both sides
-2x-19+19 = 5+19
-2x= 24
x = -24/2
x= -12
Hence x = 3, x = -12
4) ) Given |5x-3|+12 = 4
For the positive value of the function:
5x-3+12= 4
5x+9 = 4
Subtract 9 from both sides
5x+9-9 = 4-9
5x = -5
x= -1
For the negative function:
-(5x-3)+12= 4
Open the parentheses
-5x+3+12 =4
-5x+15 = 4
Subtract 15 from both sides
-5x+15-15 = 4-15
-5x = -11
x = 11/5
Hence x = -1, x = 11/5