Step 1: Distribute
-40a - 5 + 6 = 281
Step 2: Combine Like Terms
-40a + 1 = 281
Step 3: Move Variables and Constants to Different Sides
-40a = 280
Step 4: Divide
a = -7
Hope this helps!
a = -7
Step-by-step explanation;-5 ( 8a + 1 ) + 6 = 281
Step 1 :- Distribute -5 through parantheses.
-5 × 8a + 5 × 1 + 6 = 281-40a - 5 + 6 = 281Step 2 :- Combine like terms.
-40a + 1 = 281Step 3 :- Move constant to right-hand side and change their sign.
-40a = 281 - 1Step 4 :- Subtract the numbers.
-40a = 280Step 5 :- Divie both side by -40 .
-40a / -40 = 280 / -40a = -7$66.25 divided among 4 people
Circle Theorems 1! need help
Answer:
45°
Step-by-step explanation:
<lmk=90°
angles in a triangle add up to 180
45+90+<o=180
<o=180-135
<o=45
Answer:
∠ O = 45°
Step-by-step explanation:
The angle between the tangent and the radius at the point of contact is 90°
The sum of the 3 angles in Δ OML is 180° , then
∠ O = 180° - (90 + 45)° = 180° - 135° = 45°
Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns 12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?
Answer:
900 at 12%
2100 at 10%
Step-by-step explanation:
Let x= amount invested at 12%
let y= amount invested at 10%
with that being said we can write the two equation
Equation 1: x+y=3000
Equation 2: 3000*.106=.12x+.1y
isolte x from equation 1
x= 3000-y
plug this into equation 2
318=.12(3000-y)+.1y
318=360-.12y+.1y
-42= -.02y
y= 2100
Plug this into equation 1
x+2100=3000
x=900
she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.
How to determine How much money should she put into each accountLet's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.
The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).
For the 12% account:
Interest_12% = \(x \times 0.12 \times 1\) (1 year)
For the 10% account:
Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)
Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:
\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)
\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)
Now, solve for \(x\):
\(318 = 0.12x + 300 - 0.10x\)
\(318 = 0.02x + 300\)
\(18 = 0.02x\)
\(x = 900\)
Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.
Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.
Learn more about interest at https://brainly.com/question/29451175
#SPJ3
Suppose 243 subjects are treated with a drug that is used to treat pain and 52 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20% of users develop nausea.
Part A- correct answer is C.
Part B- The test statistic for this hypothesis test is ___? (Round to two decimal places as needed)
Answer:
20%?
Step-by-step explanation:
a. A CD is discounted by 10%, and then from the already discounted price, a further 15% discount is given. If the price now is $12.93, find the original price.
b. What is the total discount percent as compared to the original price?
Answer:
a. $16.90
b. 23.5%
Step-by-step explanation:
a. After the two discounts, the original price is multiplied by ...
(1 -10%)(1 -15%) = 0.90×0.85 = 0.765
Then the original price is found from ...
$12.93 = 0.765 × original price
original price = $12.93 / 0.765 ≈ $16.90
__
b. The effective discount from the original price is ...
1 -0.765 = 0.235 = 23.5%
Can you help please fellow people
Answer:
using 2 below points to draw:
(0, 7)
(3.5, 6)
Step-by-step explanation:
using
Solve, then check algebraically and graphically. 9x-3=78
Answer:
[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]
Answer:
[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]
100
During a basketball practice, Steph Curry made 234 three point shots in 45 minutes.
In the same practice, his teammate Klay Thompson made 168 three point shots in 34 minutes.
1) Find the unit rates of both players of shots made per each minute.
2) Which player was making more shots at a higher rate?
Answer:
it was very nice step so they wine so anther bed boys decided to take his legs and round and round to good boys
Angle ABC has A(3-,6), and C(9,55 as it vertices.
What is the length of side AB in units?
Answer:
7.07 units
Step-by-step explanation:
Given
[tex]A = (-3,6)[/tex]
[tex]B = (2,1)[/tex]
[tex]C = (9,5)[/tex]
See comment for complete question
Required
Side length AB
To do this, we make use of the following distance formula;
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(-3 - 2)^2 + (6 - 1)^2}[/tex]
[tex]d = \sqrt{(-5)^2 + 5^2}[/tex]
[tex]d = \sqrt{25 + 25}[/tex]
[tex]d = \sqrt{50}[/tex]
[tex]d = 7.07[/tex]
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew \$60$60dollar sign, 60 from his bank account 333 times.
What is the change in Mike's account balance after all 333 withdrawals?
\$$dollar sign
Answer:
i think that $19980 is the answer
Step-by-step explanation:
i hope it will help u
Select the correct answer. What is the range of the function shown on the graph above?
A. -8
B.-2y <-7
C. -7 Sy < -2
D. -9
Answer: The answer would be D
Step-by-step explanation:
A rectangle has dimensions of 7 in. by 5 in. Consider the solid of revolution formed when the rectangle is rotated about its 7 in. side. What is the solid formed by the revolution?
cone cylinder What is the radius (in inches) of the base of the solid of revolution?
in What is the height (in inches) of the solid of revolution?
in Find the exact volume (in cubic inches) of the solid of revolution.
Answer:
(a) Cylinder, R = 5 in, H = 7 in
(b) Volume = 549.5 cubic inches
Step-by-step explanation:
length, L= 7 in
width, W = 5 in
(a) The solid is cylinder.
Radius, R = 5 in
(b) Height = 7 in
Volume of the cylinder
[tex]V = \pi r^2 h\\\\V = 3.14 \times 5 \times 5\times 7\\\\V = 549.5 in^3[/tex]
Researchers study the relationship between interpersonal violence and health in college age women. The selected an alpha of 0.05. The researchers examined the average score on a psychological distress scale and compared the score for abused versus non abused women. A p value of 0.016 is reported. Based on this information, you know:
Answer:
There exists a relationship between interpersonal violence and health.
Step-by-step explanation:
The relationship between interpersonal violence and health :
The null hypothesis will be ; the is no relationship between interpersonal violence and health while the alternative will negate the Null ;
If no relationship exists, correlation Coefficient = 0 and if a relationship exists, then correlation Coefficient is not = 0
H0 : ρ = 0
H1 : ρ ≠ 0
α = 0.05
Reported Pvalue = 0.016
Decison region :
Reject H0 ; If Pvalue < α
Therefore, Since Pvalue < α ; we reject H0 and conclude that there exists a relationship between interpersonal violence and health.
Yellowstone National Park is a popular held trip destination. This year the senior class at
High School A and the senior class at High School B both planned trips there. The senior
class at High School A rented and filed 2 vans and 3 buses with 153 students. High
School Brented and nited il vans and 10 buses with 534 students. Every van had the
same number of students in it as did the buses. Find the number of students in each van
and in each bus.
Van: 39
Bus: 18
Van: 21
Bus: 21
o
Van: 27
Bus: 19
.
Van: 18
Bus: 39
Answer:
Who was the first president of United States?
An important factor in selling a residential property is the number of times real estate agents show a home. A sample of 15 homes recently sold in the Buffalo, New York, area revealed the mean number of times a home was shown was 24 and the standard deviation of the sample was 5 people.
a. What is the margin of error for a 98% confidence interval? (Round your answer to 3 decimal places.)
b. What is the 98% confidence interval for the population mean? (Use Student's t Distribution Table.) (Round your answers to 2 decimal places.)
Answer:
a) The margin of error for a 98% confidence interval is of 3.388 people.
b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the hypergeometric distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.
Question b:
The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people
The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.
The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
Using law of sines please show process and answer
Hello,
[tex]\widehat{A}=180^o-24.4^o-103.6^o=52^o\\\\\dfrac{sin(24.4^o)}{37.3} =\dfrac{sin(103.6^o)}{c} \\\\\\c=87.760246\approx{87.8}\\\\\\\dfrac{sin(52^o)}{a} =\dfrac{sin(24.4^o)}{37.3} \\\\\\a=71.1510189...\approx{71.2}\\[/tex]
remove bracket and simplify 6x-(3x+2)
Answer: 3x - 2
Step-by-step explanation:
First to solve this, we need to know some basic information such as:
1. (-) × (-) = +
2. (+) × (-) = -
3. (+) × (+) = +
Therefore, 6x-(3x+2)
= 6x - 3x - 2
= 3x - 2
The answer to the question after removing the bracket will be 3x - 2.
2. If 5 mg in 2 ml of liquid medication, how many mg is in 4 ml of medication?
Answer:
10mg
Step-by-step explanation:
We have a proportional relationship.
We know that there are 5mg in 2ml of liquid medication.
Now we want to know how many mg there are in 4 ml of medication.
First, we can rewrite it as:
4ml = 2ml + 2ml
And we know that, in every 2 ml of medicine, there are 5mg.
Then if we have two times 2ml of medicine, we have two times 5mg.
This is:
2*5mg = 10mg
Which of the following slopes of a line pass through points (3, 1) and (0, 1)?
The measures of two angles of a triangle are 101° and 37°. Find the measure of the third angle in degrees.
Answer:
42 degrees
Step-by-step explanation:
We already have the two angles for the triangle, we just need the third. For triangles, the can only add up to 180 degrees. 101+37=138 degrees, now we subtract 138 from 180.
180-138=42.
Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selection down to ten mysteries and twelve Nonfiction books. If she randomly chooses four books fro her selections, what’s the probability that they will all be nonfiction?
twelve nonfiction books. If she randomly chooses four books
answer to 4 decimal places, if necessary.
Answer
Answer:
0.0677 = 6.77% probability that they will all be nonfiction
Step-by-step explanation:
The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 + 12 = 22 books.
She chooses 4 books, which means that [tex]n = 4[/tex]
12 nonfiction, which meas that [tex]k = 12[/tex]
What’s the probability that they will all be nonfiction?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677[/tex]
0.0677 = 6.77% probability that they will all be nonfiction
In 1999, a company had a profit of $173,000. In 2005, the profit was
$206,000. If the profit increased by the same amount each year, find the
rate of change of the company's profit in dollars per year. *
$5,500
$4,004
$379,000
$33,000
O $102.74
Answer:
A. $5500Step-by-step explanation:
The difference of years:
2005 - 1999 = 6The difference in profit over 6 years:
206000 - 173000 = 33000Average rate of change:
33000/6 = 5500It has been 6 years,
The main difference in profit over 6 years between 1999 and 2005 is,
→ 206000 - 173000
→ 33000
Then the average rate of change is,
→ 33000/6
→ 5500
Hence, $ 5500 is the correct option.
Which list shows the following numbers in order from least to greatest: -15, 8, 4, -3, -7,
4, 8, -15, -7, -3
-15, 8, 4, -3, -7.
-15.-7.-3, 4.8
-15.-3, 4, -7.8
Where does the graph of f(x)=2√-x+2 start?
A. (−2,0)
B. (2,0)
C. (0,2)
D. (0,−2)
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a.
f(x)= 7x e^x, a= 0
Hi there!
[tex]\large\boxed{p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4}[/tex]
Recall a Taylor series centered at x = 0:
[tex]p(x) = f(0) + f'(0)(x) + \frac{f''(0)}{2}x^{2} + \frac{f'''(0)}{3!}x^{3} + ...+ \frac{f^n}{n!}x^n[/tex]
Begin by finding the derivatives and evaluate at x = 0:
f(0) = 7(0)e⁰ = 0
f'(x) = 7eˣ + 7xeˣ f'(0) = 7e⁰ + 7(0)e⁰ = 7
f''(x) = 7eˣ + 7eˣ + 7xeˣ f''(0) = 7(1) + 7(1) + 0 = 14
f'''(x) = 7eˣ + 7eˣ + 7eˣ + 7xeˣ f'''(0) = 21
f⁴(x) = 7eˣ + 7eˣ + 7eˣ + 7eˣ + 7xeˣ f⁴(0) = 28
Now that we calculated 4 non-zero terms, we can write the Taylor series:
[tex]p(x) = 0 + 7x + \frac{14}{2}x^2 + \frac{21}{3!}x^3 + \frac{28}{4!}x^4[/tex]
Simplify:
[tex]p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4[/tex]
A system of equations is said to be redundant if one of the equations in the system is a linear combination of the other equations. Show by using the pivot operation that the following system is redundant. Is this system equivalent to a system of equations in canonical form?
a) x1 +x2 −3x3 = 7
b) −2x1 +x2 +5x3 = 2
c) 3x2 −x3 = 16
Answer:
prove that The given system of equations is redundant is attached below
Step-by-step explanation:
System of equations
x1 +x2 −3x3 = 7
−2x1 +x2 +5x3 = 2
3x2 −x3 = 16
To prove that the system is redundant we will apply the Gaussian elimination ( pivot operation )
attached below is the solution
Multiply and show work
Answer:
-15m^10 -38m8+57m^6+98m^4-30m^2
Answer:
jere is your answer i hope it will help u
Help me on this please
Answer:
x = 3.5
Step-by-step explanation:
Triangle to the right:
4^2 + x^2 = 8^2
16 + x^2 = 64
y^2 = 48
Triangle to the left:
x^2 + 6^2 = 48
x^2 + 36 = 48
x^2 = 12
x = sqrt(12)
x = 3.5
9. What is the value of x if the quadrilateral is a rhombus? 15 5x 4x+3
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
Required:
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
c. What is the 95% confidence interval estimate of the difference between the two population proportions?
d. What is your conclusion?
Answer:
b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2
c)CI 95 % = ( 0.00002 ; 0.09998)
Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.
Recent Sample
Sample size n₁ = 1000
Number of events of people with financial fitness more than fair
x₁ = 410
p₁ = 410/ 1000 = 0.4 then q₁ = 1 - p₁ q₁ = 1 - 0.4 q₁ = 0.6
Sample a year ago
Sample size n₂ = 1200
Number of events of people with financial fitness more than fair
x₂ = 420
p₂ = 420/1200 p₂ = 0.35 q₂ = 1 - p₂ q₂ = 1 - 0.35 q₂ = 0.65
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
CI 95 % then significance level α = 5% α = 0.05 α/2 = 0.025
To calculate p-value:
SE = √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂
SE = √ 0.4*0.6/1000 + 0.65*0.35/1200
SE = √ 0.00024 + 0.000189
SE = 0.021
z(s) = ( p₁ - p₂ ) / SE
z(s) = ( 0.4 - 0.35 )/0.021
z(s) = 0.05/ 0.021
z(s) = 2.38
We find p-value from z-table to be p-value = 0.00842
Comparing
p-value with α/2 = 0.025
α/2 > p-value
Then z(s) is in the rejection region for H₀. We reject H₀
CI 95 % = ( p₁ - p₂ ) ± 2.38*SE
CI 95 % = ( 0.05 ± 2.38*0.021 )
CI 95 % = ( 0.05 ± 0.04998)
CI 95 % = ( 0.00002 ; 0.09998)
CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate