Answer:
D. ([tex]y^{3}[/tex] + 2)
Step-by-step explanation:
A factor of an expression can either be in the form of an algebraic expression, alphabet or number. In the question, the given expression can be written as;
7[tex]z^{4}[/tex] - 5 + 10[tex]y^{3}[/tex] + 20
Factorizing the expression gives;
7[tex]z^{4}[/tex] - 5 + 10([tex]y^{3}[/tex] + 2)
Therefore, it would be observed that the factor in the expression is;
([tex]y^{3}[/tex] + 2)
Simplify. Rewrite the expression in the form 7^n7 n 7, start superscript, n, end superscript. \left(7^3\right)^{3}=(7 3 ) 3 =left parenthesis, 7, cubed, right parenthesis, cubed, equals
Step-by-step explanation:
We need to write the given expression in the form of [tex]7^n[/tex] and the expression is [tex](7^3)^3[/tex].
The property is : [tex](x^n)^m=x^{nm}[/tex]
We have, x = 7, n = m = 3
So,
[tex](7^3)^3=7^{3\times 3}\\\\=7^9[/tex]
Therefore, the value of n is 9.
Solve for x with work
Answer:
47 degrees
Step-by-step explanation:
The two angles shown are "vertical angles" and thus are equal.
Thus, 2x + 3 = x + 50
Combining like terms, we get:
x = 47 degrees
5. Tia invests $2,500 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 5 years? Look at the concept summary if you forgot the formula for compound interest.
Answer:
$3050.48
Step-by-step explanation:
If 4% is compounded quarterly, that means it's 1% every quarter. since we have 5 years, that's 1.01^20, which is approx. 1.2202. We multiply this by the orignal $2500, so our investment at the end of 5 years is $3050.48 (rounded to nearest cent)
The amount of money that Tia's investment would be worth at the end of 5 years is equal to $3050.5.
Given the following data:
Principal = $2,500Interest rate = 4% = 0.04Time = 5 yearsNumber of times = 4To determine how much is the investment worth at the end of 5 years:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value.P is the principal (starting amount).r is annual interest rate.n is the number of times the interest is compounded in a year.t is the number of years for the compound interest.Substituting the given parameters into the formula, we have;
[tex]A = 2500(1 + \frac{0.04}{4})^{4\times 5}\\\\A = 2500(1 +0.01)^{20}\\\\A = 2500(1.01)^{20}\\\\A = 2500(1.2202)[/tex]
Future value, A = $3050.5
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A new cell phone costs $85, and the sales tax is 9%. What is the amount of the sales tax?A new cell phone costs $85, and the sales tax is 9%. What is the amount of the sales tax?A new cell phone costs $85, and the sales tax is 9%. What is the amount of the sales tax?
Step-by-step explanation:
Sales tax = $7.65
Explanation:
To find the sales tax, you would find 9% of $85
$85×9÷100 (You can reduce 85 and 100 because they have a common factor of 5)
$17×9÷20 (Multiply 9×17)
153÷20 = $7.65
Answer:
7.65
Step-by-step explanation:
8y + 10=42 solve for y
Answer: y=4
Step-by-step explanation:
Step 1: Subtract 10 from both sides.
8y+10−10=42−10
8y=32
Step 2: Divide both sides by 8.
8y
8
=
32
8
y=4
Answer:
8y + 10 =42
8y = 42-10
8y = 32
8y/8 = 32/8
y = 4
Suppose you run 5 miles from your house to a friend's house at a speed of 6 miles per hour. When the time comes to return home, you are tired and walk the same 5 miles home at 3 miles per hour. How long did you spend running to your friend's house?
Answer:
2hours and 30minutes
Step-by-step explanation:
6mph for 5 miles, would be 10 minutes per mile(in an hour because of 60). Only five were completed to itd take 50 minutes. 3mph for 5hours would take 1hr and 40 minutes because 3miles would take 1 hour which would make one mile take 20 minutes so you add the two twenties(for the last two miles) to get 40. Then u add them together. (50min+60min+40min)
Evaluate the integral. W (x2 y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 1) and base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)
Answer:
[tex]\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}[/tex]
Step-by-step explanation:
Given that:
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz[/tex]
where;
the top vertex = (0,0,1) and the base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)
As such , the region of the bounds of the pyramid is: (0 ≤ x ≤ 1-z, 0 ≤ y ≤ 1-z, 0 ≤ z ≤ 1)
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 \int ^{1-z}_0 (x^2+y^2) \ dx \ dy \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 ( \dfrac{(1-z)^3}{3}+ (1-z)y^2) dy \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^3}{3} \ y + \dfrac {(1-z)y^3)}{3}] ^{1-x}_{0}[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^4}{3}+ \dfrac{(1-z)^4}{3}) \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz =\dfrac{2}{3} \int^1_0 (1-z)^4 \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz =- \dfrac{2}{15}(1-z)^5|^1_0[/tex]
[tex]\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}[/tex]
Find the volume of a cube if an edge has lenght 3xyz
Answer:
27x³y³z³
Step-by-step explanation:
The volume of a cube is the cube of the edge length:
V = (3xyz)³ = 3³x³y³z³
V = 27x³y³z³
This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10 , with repeats allowed. (a) Choose four numbers that have the smallest possible standard deviation. What is s in this case? (Enter your answer rounded to the nearest whole number.)
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following instructions :
Choose 4 numbers from the whole numbers 0 - 10
Note : Repetition is allowed
Choose 4 numbers with the smallest possible standard deviation.
The smallest possible value of standard deviation obtainable is 0;
Hence in other to obtain a standard deviation value of 0, then;
The mean squared deviation value must be zero (0)
Σ(X - mean)^2 = 0
To achieve this, the values of X and the mean must be the same.
Hence all 4 numbers (X) must be the same in other to have a mean value which is equal to X
For instance :
If X = 3, 3, 3, 3 (since Repetition is allowed)
Man value = (3+ 3+ 3+ 3) / 4 = 12 / 4 = 3
Σ(3 - 3)² = 0 for all values of x
√Σ(x - mean)² / n = 0 ; if all values of x are the Same
n = Number of observations
A possible list of values is (3,3,3,3)
IF nominal alpha is set to .01, which of these p values would be considered criteria for rejecting the null hypothesis?
a. .002
b. .009
c. .04
d. .042
Answer:
The null hypothesis gets rejected for the p-value of 0.04 and 0.042.
Step-by-step explanation:
We are given the level of significance of [tex]\alpha[/tex] = 0.01 or 1%. And also we are provided with the different p-values.
As we know that; the decision rule for rejecting the null hypothesis is given by;
If the P-value of our test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.If the P-value of our test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis.(i) The P-value given is 0.002.
Here, the P-value is less than the level of significance as 0.002 < 0.01, then we have sufficient evidence to reject our null hypothesis. So, the null hypothesis gets rejected.
(ii) The P-value given is 0.009.
Here, the P-value is less than the level of significance as 0.009 < 0.01, then we have sufficient evidence to reject our null hypothesis. So, the null hypothesis gets rejected.
(iii) The P-value given is 0.04.
Here, the P-value is more than the level of significance as 0.04 > 0.01, then we have insufficient evidence to reject our null hypothesis. So, the null hypothesis does not get rejected.
(iv) The P-value given is 0.042.
Here, the P-value is more than the level of significance as 0.042 > 0.01, then we have insufficient evidence to reject our null hypothesis. So, the null hypothesis does not get rejected.
Set of integers between -12 and 12
Answer:
0
Step-by-step explanation:
prove that 3^2n+7 is divisible by 8
Answer:
Step-by-step explanation:
If n=1 then 32n+7=16=2(8) so true when n=1
Assume true for n=k so
8|32k+7
If n=k+1
32(k+1)+7
32k+2+7
If 32n+7 is divisble by 8 then 32n+7=8A where A∈Z, and thus 32k+2+7=8B where B∈Z
32×32k+7
32×(8A)=72A
72A=8(9A)=9B
So by induction 32n+7 is divisibe by 8 ∀n∈N
Which property would allow you to use mental computation to simplify the problem 27 + 15 + 3 + 5? additive identity additive inverse commutative property of addition distributive property
Answer:
Commutative Property
Step-by-step explanation:
Additive Identity: If you add a real number to zero or add zero to a real number, then you get the same real number back.
Additive Inverse: When you add the same number but reversed sign, you get 0.
Commutative Property: a + b = b + a
Addition distributive property: a(b+ c) = ab + ac.
In this case, we use the commutative property:
27 + 15 + 3 + 5 = 27 + 3 + 15 + 5.
We know that 27 + 3 = 30 and 15 + 5 = 20, so we get 50 quickly using mental math.
Answer:
Communitive
Step-by-step explanation:
3(x2 + x + 2) +5(x-4)
I need this urgently anyone knows this?
Answer:
A/( 1+rt) = P
Step-by-step explanation:
A = P ( 1+rt)
Divide each side by ( 1+rt)
A/( 1+rt) = P ( 1+rt)/(1+rt)
A/( 1+rt) = P
Use an integer to express the number representing a change.
From 2011 to 2012, attendance at a sports game went from 49,552 to 47,186, a decrease of 2,366
The integer is ?
Answer:
-2366
Step-by-step explanation:
Given
2011 Attendance = 49,552
2012 Attendance = 47,186
Required
Determine the integer that represents the change
Calculate the difference between both attendance
[tex]Change = 2011\ Attendance - 2012\ Attendance[/tex]
[tex]Change = 49552 - 47186[/tex]
[tex]Change = -2366[/tex]
Calculating the difference, we have -2366
Conclusively; the integer that represents the change is -2366
(b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations?
Answer:
>0.95
Step-by-step explanation:
This probably refers to a normal distribution. In a normal distribution, according to the empirical rule,
68% of observed data falls within 1 standard deviation of the mean
95% falls within 2 standard deviations of the mean
99.7% falls within 3 standard deviations of the mean
In this case, the observed data is distance and the average figure for all observed distances is the mean distance.
So, the probability that a/any distance observed exceeds the mean distance by more than 2 standard deviations is >95%
In other words, the probability is >0.95
Need help plzzz anyone
Answer:
A) √61
Step-by-step explanation:
a²+b²=c²
(4-(-2))²+(5-0)²=c²
6²+5²=c²
36+25=c²
61=c²
c=√61
The sum of two numbers is zero. One number is six less than twice the other. Find the numbers. (Enter your answers as a comma-separated list.)
Answer:
2,-2
Step-by-step explanation:
firsr number = x
second number = 2x-6
x+2x-6=0
3x-6=0
3x=6
x=2
first number=x=2
second number=2x-6=-2
Need help I don’t understand
Answer:
58 degrees
Step-by-step explanation:
subtract 122 from 180
the ans of your above questions is 58°
ID: A
17. N.Q.1-2 ULHS has a student that can run 100 yds in 15 seconds. Mrs. Duke's class converted his speed to
miles per hour below and determined he can run 4.55 miles per hour. Is the conversion correct? If not, explain
what the class did wrong and then work it out using dimensional analysis. You MUST Show all work.
100 yds
60 sec
60 min 1 mile
= 4.55 mph
15 sec
1 min 1 hr 5280 yds
Answer:
13.63 miles per hour
Step-by-step explanation:
100 yards / 15 sec converted to miles per hour
100 yards x 60 sec x 60 min x 1 mile = 13.63 miles/hr
15 sec 1 min 1 hr 1760 yards
the mistake on Mrs Dukes is the conversion from miles to yards.
1 mile = 1760 yards NOT 5280 yards
mg+rg=2H, solve for g
Answer:
g = 2H/(m + r)
Step-by-step explanation:
mg + rg = 2H
g(m + r) = 2H
(g(m + r))/(m + r) = 2H/(m + r)
g = 2H/(m + r)
The required solution of the algebraic expression for g is 2h / (m + r ).
Given that,
To simplify the algebraic expression mg+rg=2H for g,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
the given algebraic expression is,
mg + rg = 2h
taking g common on left side,
g(m + r) = 2h
transposition of the term (m + r) to the denominator of the right-hand side,
g = 2h / (m + r)
The above expression is the required solution for the g.
Thus, the required solution of the algebraic expression for g is 2h / (m + r ).
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Lin recorded 14,-7 and 9. what was the net gain or loss?
Answer:
12345
Step-by-step explanation:
I need helpp thxxxxx
Answer: x=12
Step-by-step explanation:
5x=4x+12
move all terms containing x to the left side of the equation
subtract 4 from 5
1x=12
x=12
Can someone show me step by step how to solve this problem? I’m stuck on how to do this. 5/6x +3 > -7 (1/6x +3)
Answer:
x>-12
Step-by-step explanation:
first you would simplify by multiplying -7 from the terms in the parenthesis and then you would get [tex]\frac{5x}{6} +3>\frac{-7x}{6} -21[/tex] then you would add 21 to both sides to get rid of the -21 and you would get [tex]\frac{5x}{6} +24>\frac{-7x}{6}[/tex] then you would subtract 5/6 from both sides to get rid of the 5/6 so you get 24>[tex]\frac{-12x}{6}[/tex] and then you would simplify by multiplying 6 to both sides so you get 144>-12x then you would divide both sides by -12 (note that you have to flip the greater than or less then sign after dividing by a negative number) so you get -12<x or x>-12
What is the value of the expression?
10+|5+2|
A. 3
B. -17
C. -3
D. 17
Answer:
17
Step-by-step explanation:
Because 10+5=15+2=17
Solve for z.
Z<-9
Z>-9
Answer:
z>-9
Step-by-step explanation:
Answer: z > -9
Step-by-step explanation:
[tex]\frac{-2z-3}{3} < 5[/tex] multiply each side by 3 to get
-2z -3 < 15 now add 3 to both sides
+3 +3
-2z < 18 Divide both sides by -2. Since your dividing by a negative number the inequality sign will change
z> -9
An outdoor spa (hot tub) draws 1504 watts to keep the water warm. If the utility company charges $0.14 per kilowatt-hour, how much does it cost to operate the spa for four months during the winter (24 hours per day)? Assume each month has 30 days.
Answer:
$606.41
Step-by-step explanation:
1504 W * (1 kW)/(1000 W) * 0.14 $/(kW*h) * 4 months * (30 days)/(month) * (24 hours)/day =
= $606.41
If Mitzi has two dogs, a puppy that weighs 25 pounds and an adult that weighs 80 pounds, how much will it cost to bathe them both? $105 $115 $150 $160
Answer:
The correct answer is A) $105
Step-by-step explanation:
In this real-world problem, the cost to groom both dogs is (the puppy) + (the adult dog) = x.
For the first step, y = 40, if x <= 25.
y = 50, if 25 < x < 50.
if x >= 50, then y = 0.50x + 25
So therefore, substitute the puppy + adult dog = x
25 + 80 = x
105 = x
So, the final answer is $105.
It's on Edgen.
Answer:
A) 105
Step-by-step explanation:
Edg Brainliest
Tell whether each equation is True, False, or Open. Explain. "must explain for credit"
1. 6-t=12
2. 7+(-5)=12
3. 31 - 15 = 22 + (-3)2