Answer:
4, -2
Step-by-step explanation:
Hello, please consider the following.
[tex]\begin{aligned}4x^2-8x-32=0 &\text{ ***We divide by 4.***}\\\\x^2-2x-8=0 &\text{ ***We complete the square. ***}\\\\(x-1)^2-1-8=(x-1)^2-9=0 &\text{ ***We move the constant to the right.***}\\\\(x-1)^2=9=3^2 &\text{ ***We take the root.***}\\\\x-1=\pm3 &\text{ ***We add 1.***}\\\\x=1+3=\boxed{4} \ & or \ x=1-3=\boxed{-2}\end{aligned}[/tex]
Thanks
A rectangular bird feeder costs $18.00. A cylindrical bird feeder costs $24.00. The expected cost to keep the rectangular bird feeder filled is $3.00 per week. The expected cost the keep the cylindrical bird feeder filled is $2.00 per week. The equation below models the break-even point. 18 + 3x = 24 + 2x What does x represent? the total cost to fill the rectangular bird feeder after any number of weeks the total cost to fill the cylindrical bird feeder after any number of weeks the number of weeks the bird feeders are filled the number of bird feeders purchased each week
Answer:
the number of weeks the bird feeders are filled
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Just took the review
A new restaurant, Banana Monkey, has been open for two weeks. The number of diners who have eaten at the restaurant on each of those days is shown in the plot below. Number of diners Stem 7. 8 9 Leaf 6 6 8 9 2 5 5 8 8 9 4 7 7 7 Key 8 7 = 87 How many days did Banana Monkey have more than 85 guests?
Answer:
to much numbers
Step-by-step explanation:
Need Help This Is A Tricky One
Answer:
28th floor........
Step-by-step explanation:
...
Answer:
28
Step-by-step explanation:
current position: 9
down 4 floors: 9-4 = 5
up 7 floors: 5+7 = 12
up 8 floors: 12+8 = 20
up 8 floors: 20+8 = 28
Solve application problems using quadratic equations. 1. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 96. Find the numbers.
Hello, let's note a the positive real number.
A positive real number is 4 less than another.
So, the other number is a - 4
When 8 times the larger is added to the square of the smaller, the result is 96.
So, we need to solve the following equation.
[tex]8a+(a-4)^2=96[/tex]
Let's do it!
[tex]8a+(a-4)^2=96\\\\8a+a^2-8a+16=96\\\\a^2=96-16=80=4^2*5\\\\a=\pm4\sqrt{5}[/tex]
As a is positive, there is only one solution which is.
[tex]\Large \boxed{\sf \bf \ \ a=4\sqrt{5} \ \ }[/tex]
Thank you.
The amount given by the sum of numbers can be presented in an equation
form from which the value of each number can be obtained.
The large number is 4·√5, the smaller number is 4·(√5 - 1)
Reason:
Let x represent the large number, we have;
The smaller number = x - 4
8 × x + (x - 4)² = 96
8·x + (x - 4)² = 96
Required:
The values of the numbers
Solution:
8·x + (x - 4)² = 8·x + x² - 8·x + 16 = 96
8·x - 8·x + x² + 16 = 96
x² + 16 = 96
x² = 96 - 16 = 80
x = ±√(80) = ±4·√5
Given that the numbers are positive, we have;
The large number, x = 4·√5
The smaller number = x - 4 = 4·√5 - 4
The smaller number = 4·√5 - 4 = 4·(√5 - 1)
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What is the value of x that makes the given equation true? x−3x=2(4+x)
the answer to your question is x= -2
Marcus bought w childrens's movie tickets for $5 each and n adult's movie tickets for $11 each. Write an algebraic expression for total amount Marcus spent.
Answer:
5w+11n
:D
Hope this helped!
My regards
Y A chemist can purchase a 10% saline solution in 500 cubic centimeter containers, a 20% saline solution in 500 cubic centimeter containers, and a 50% saline solution in 1,000 cubic centimeter containers. He needs 12,000 cubic centimeters of 30% saline solution. How many containers of each type of solution should he purchase in order to form this solution
Step-by-step explanation:
ultimately you need to end up with 30% solution
with 10%, 20%, and 50%, you are forced to tamper with the various percentages to reach the desired goal.
Since it is an even 12,000 (i.e. no 12500) and you have no hard container volumes to deal with, therefore find the easiest combination to reach 30%. In this case, (10%+50%)/2 = 30%
So therefore you need 12000 cubic centimeters of liquid, half of it being 50% and half being 10%.
12000/2 = 6000 cubic centimeters each
for 50%, each container is 1,000 cubic centimeters, so 6000/1000 =6 containers for 10% each container is 500 cubic centimeters, so 6000/500 = 12 containers
Therefore, you need 6 containers of 50% solution and 12 containers of 10% solution.
Question 1
Solve the equation.
-9h= - 27
Answer:
h=3
Step-by-step explanation:
-9h= - 27
Divide each side by -9
-9h/-9= - 27/-9
h = 3
Answer:
h = 3
Step-by-step explanation:
Step 1: Divide both sides by -9
[tex]\frac{-9h}{-9} =\frac{-27}{-9} \\h=3[/tex]
Therefore the h = 3
Find the range of the given data set. 5/8, 3/4, 1 1/8, 1 1/4 A)5/8 B)3/4 C)1 1/8
Answer:
A)5/8
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.Given data set:
5/8, 3/4, 1 1/8, 1 1/4Rewriting the data set in the same denominator to compare:
5/8, 6/8, 9/8, 10/8As we see the smallest value is 5/8 and the highest value is 10/8, so the difference:
10/8 - 5/8 = 5/8So, the range of the given data set is 5/8
Correct choice is: A)5/8
Landon usually eats two slices of pizza from a 12 inch pizza cut into 6 slices. I make homemade pizza on a rectangular cookie sheet that is 10 inches by 15 inches and I cut it into 8 rectangular pieces. How many slices of this homemade pizza will Landon proabably eat
Answer:
He will eat 0.233 of one slice
Step-by-step explanation:
If Landon eats only two slices of pizza from a 12 inch pizza cut into 6
It means each slice has 2 inch pizza and Landon eats 2 of these
So Landon eats 2*2 = 4 inch pizza
So a rectangular pizza of 10 by 15
= 10*15
= 150 inch pizza
Cut into 8 slices
= 150/8
.= 18.75 inch per slice
4/18.75 = 0.233
He will eat 0.233 of one slice
A university law school accepts 6 out of every 11 applicants. If the school accepts 552 students find how many applicants they received
Answer:
1012
Step-by-step explanation:
The ratio of student / applicant is 6 /11
So for 552 students, the applicants number is:
6/11 = 552/xx = 552*11/6 x= 1012Number of applicants is 1012
The statewide pass rates for ENGL&101 across Washington state community colleges is 68%. An instructor in the English department at CBC believes rates at CBC may be higher than the state average. This study can be stated as a formal hypothesis test in the following way:
H0 : p=0.68
HA: p > 0.68
To perform his study, he took a random sample of 250 students at CBC that had taken
ENGL&101, and found that 179 had passed the course.
Using your g from the last question, calculate the test statistic for the hypothesis test. Round your answer to two decimal places.
Answer:
The calculated value Z=1.2413 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
An instructor in the English department at CBC believes rates at CBC may be equal to the state average
Step-by-step explanation:
Step(i):-
Given Population proportion
P=68%= 0.68
Sample proportion
[tex]p^{-} =\frac{x}{n} = \frac{179}{250} = 0.716[/tex]
Null hypothesis : H₀ : p = 0.68
Alternative Hypothesis :H₁ : p > 0.68
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.716-0.68 }{\sqrt{\frac{0.68 X 0.32}{250} } }[/tex]
Z = 1.2413
Level of significance
[tex]Z_{0.05} = 1.96[/tex]
The calculated value Z=1.2413 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
An instructor in the English department at CBC believes rates at CBC may be equal to the state average
Cuanto es la raíz cuadrada de 25
Find the odds in favor of rolling the sum of 10 when rolling a pair of dice
A 11 to 1
B 1 to 3
C 1 to 11
D 3 to 1
Answer:
C 1 to 11
Step-by-step explanation:
When rolling 2 dice, there are 36 possible outcomes.
The outcomes that have a sum of 10 are:
4, 6
5, 5
6, 4
There are 3 outcomes of 10 and 33 outcomes of not 10.
Odds of outcome of 10:
3:33 = 1:11
1 to 11 is the odds in favor of rolling the sum of 10 when rolling a pair of dice option (C) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A standard dice is rolled:
The total number of outcomes(two dice are rollling) = 6x6 = 36
The outcomes that have a sum of 10 = ({4, 6}, (5, 5), (6, 4)}
The total number of outcomes = 3
Total outcomes(after removing 3 outcomes that have a sum of 10)
= 36 - 3 = 33
Odds of outcomes = 3
The odds in favor = 3/33 = 1/11 or 1 to 11
Thus, 1 to 11 is the odds in favor of rolling the sum of 10 when rolling a pair of dice option (C) is correct.
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Write a decimal expansion for 2/9. Chose the correct decimal notation.
Answer:
This is the answer
2/9=0.222222222.
Answer:
.2222 ( repeating)
Step-by-step explanation:
The values in the following matrix are treatment means from a two-factor study. One of the means is missing. What value for the missing mean would result in no main effect for Factor A?
B1 B2
A1 6 8
A2 12 ?
a. 14
b. 10
c. 12
d. 2
(Please explain)
Answer: D) 2
the value for the missing mean would result in no main effect for Factor A is 2
Step-by-step explanation:
Given that;
B1 B2
A1 6 8
B1 12 ?
To find the missing mean;
lets missing mean be x
Here mean of A1
( 6 + 8 ) / 2 = 14 / 2 = 7
Now mean of A2
(12 + x ) / 2 = 7
x + 12 = 14\x = 14 -12 = 2
Therefore the value for the missing mean would result in no main effect for Factor A is 2
so option d) is the correct answer
Answer:
b
Step-by-step explanation:
Is the number 25/9 irrational?
Answer:
Step-by-step explanation:
No; it is rational. 25/9 is the ratio of two integers.
Explanation:
We have a fraction of two integers, so 25/9 is rational. A rational number is any fraction of two integers (as long as the denominator is not zero).
Something that is irrational would be pi = 3.14159... where we cannot write it as a fraction of two integers. We can get approximations such as 22/7, but we cannot land exactly on pi with a fraction like this. Another irrational value is sqrt(2).
Something like sqrt(25) is rational though because sqrt(25) = 5 = 5/1.
Solve the equation. 5/7p - 2/7p + 12 = 6
Answer:
p = -14
Step-by-step explanation:
5/7p - 2/7p + 12 = 6
Combine like terms
3/7 p +12 = 6
Subtract 12 from each side
3/7p + 12-12 = 6-12
3/7p = -6
Multiply each side by 7/3
7/3 * 3/7p = -6*7/3
p = -14
Answer:
p = - 14
Step-by-step explanation:
5/7p - 2/7p + 12 = 6
subtract 12 both sides
5p/ 7 - 2p/7 + 12 = 6 - 12
simplify
5p/7 - 2p/7 = -6
multiply both side by 7
5p/7 * 7 - 2p/7 * 7 = -6 * 7
simplify
5p - 2p = -42
p = -42 / 3
p = - 14
5. A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci. a) In testing the scientist's belief, write the appropriate hypotheses at 0.05 level of significance.
Complete Question
A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4 pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.
a) In testing the scientist's belief, write the appropriate hypotheses:
[tex]H_o:[/tex] Ha:
b) What decision should be made?
Answer:
a
The null hypothesis is [tex]H_o : \mu \le 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
b
There is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 4 \ pci[/tex]
The sample size [tex]n = 36 \ days[/tex]
The sample mean is [tex]\= x = 4.4 \ pci[/tex]
The standard deviation is [tex]\sigma = 1 \ pci[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t =2.4[/tex]
The p-value is mathematically represented as
[tex]p-value = P(Z > 2.4 )[/tex]
From the z-table
[tex]P(Z > 2.4 ) = 0.008[/tex]
[tex]p-value =0.008[/tex]
So from this obtained value we see that
[tex]p-value < \alpha[/tex] so we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Sara bought a pair of shoes that were $64 but were on sale for $46. Sales tax is 6%. How much did she pay for the shoes?
Answer:
$48.76
Step-by-step explanation:
So, Sara bought the pair of shoes for $46 due to a discount.
Sales tax was 6% or 0.06. In other words, she had to pay 0.06(46)=2.76 for tax.
Thus, the total amount Sara paid for the shoes is $46+$2.76=$48.76
A line has the equation y = 3x + 4.
(a) This line has slope 3/1
(b) Any line parallel to this line has slope
(c) Any line perpendicular to this line has
Answer:
b. 3/1 c. -1/3
Step-by-step explanation:
When a line is parallel to another they don't intersect and instead go in the same direction. Therefore they have the same slope
b. 3/1
When a line is perpendicular it has to be the negative reciprocal. This means that it you have to flip the numbers in the fraction and make it negative (unless it is already negative, then it becomes positive)
c. -1/3
At the dairy farm, two cows produce enough milk to fill 7 equal sized buckets. Each cow produces the same amount of milk. What is the rate per bucket per cow?
Answer:
3.5 buckets per cow
Step-by-step explanation:
Given
[tex]Buckets = 7\ equal\ sized[/tex]
Required
Determine the rate per bucket per each cow
From the question, we understand that both cows produced same quantity of milk;
And since, they're are two cows
Milk produced by each cow is calculated by dividing number of buckets by 2; as follows;
[tex]Each\ cow = \frac{7}{2}\ buckets[/tex]
[tex]Each\ cow = 3.5\ buckets[/tex]
Hence, the rate is 3.5 buckets per cow
19. In each of the following ligures, find the values of x and y
Answer:
x and y is 115 exterior angle property
Answer:
[tex]\boxed{x = 65, y=50}[/tex]
Step-by-step explanation:
→ We know that angles on a straight line add up to 180° so we can use that to work out angle x
x + 115° = 180°
⇒ Minus 115° from both sides to isolate x
x = 65°
→ We can see that there are 2 angles labelled x so we can use that to find the value of y
65° × 2 = 130°
→ We utilise the angle fact that angles in a triangle add up to 180°
130° + y = 180°
⇒ Minus 130° from both sides to isolate y
y = 50°
If there were 1,000 cars in a line with an average car length of 10.8 feet, how long would the line be in feet? Assume that the cars are lined up bumper-to-bumper.
Answer:
10,800 feet
Step-by-step explanation:
1000 * 10.8 because there are 1000 cars each 10.8 feet long
Use the Distance Formula to find the distance between the two points in polar coordinates. (Round your answer to one decimal place.) (8, 0.2), (9, 1.7)
Answer:
Distance= 1
Step-by-step explanation:
Distance be points using polar coordinates
Distance= √(8² +9² -2(8)(9)cos(0.2-1.7)
Distance=√(64 + 81-(144)cos(-1.5))
Distance= √(145-143.9506)
Distance=√ 1.0493
Distance= 1.0243
Distance= 1
Meghan is making fruit salads and fruit smoothies. The salad recipe calls for 1/6 cup of strawberries, and the smoothie recipe calls for 2/3 cup strawberries. If Meghan wants to make 2 fruit salads and 2 fruit smoothies, how many cups of strawberries does she need?
Answer:
5/3 cup(s)
Step-by-step explanation:
Meghan needs 5/3 cups of strawberries to make 2 fruit salads and 2 fruit smoothies.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Need of cup of strawberries for making one fruit salad recipe = 1/6,
And need of cup of strawberries for making one fruit smoothie recipe = 2/3.
To make 2 fruit salads,
Need of cup of strawberries = 2 x 1/6 = 1 / 3
To make 2 fruit smoothies,
Need of cup of strawberries = 2 x 2/3 = 4/3
Total number of cups of strawberries = 1/3 + 4/3 = 5/3
Meghan needs 5/3 cups of strawberries.
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pls answer asap!! will mark brainliest giving 50 points ty ily <3
Answer:
56
Step-by-step explanation:
Keep the order of opperations in mind when doing this (PEMDAS). First, solve what is inside the parentheses (6-1). Then, solve the exponent and the multiplication (6² and 5×5). Finally, finish adding and subtracting to get the answer.
Answer:
56
Step-by-step explanation:
Hello!
We have to follow the order of PEMDAS
Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction
5 x 5 - (6 - 1) + [tex]6^{2}[/tex]
Parenthesis First
[tex]5 x 5 - (5) + 6^2[/tex]
Exponents next
[tex]5x5 - (5) + 36[/tex]
Multiplication and Divsion from left to right
25 - (5) + 36
Addition and Subtraction from left to right
20 + 36
56
The answer is 56
Hope this Helps!
Which of the following numbers is not a
prime number?
A. 2
C. 11
B. 3
D. 27
Answer:
27, it is divisible by 1, 3, 9, and 27
Step-by-step explanation:
What is the inverse function of f(x) = x
Answer:
y = x
Step-by-step explanation:
The inverse of f(x) = x is just y = x.
Daniel says that when the irrational number 7√3 is multiplied by any rational number, the product is always an irrational number. What value for the rational number disproves Daniel's claim?
Answer: 0
============================================
Explanation:
When we multiply 0 by any number, we get 0 as a result
x*0 = 0
0*x = 0
for any number x.
The number 0 is rational since we can write it as a fraction of two integers
0 = 0/1
If Daniel were to correct his statement to say "multiply by any nonzero rational number", then his statement would be correct that the result is irrational.
----------------------------------------------
Extra info:
Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers
Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero
Let q be an irrational number. We cannot write q as a ratio of two integers
The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s
This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.
Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.