Solve the quadratic function by completing the square. What are the missing pieces in the steps?
_32 = 2(x2 + 10x)
Answer:
Step-by-step explanation:
-32 = 2(x² + 10x)
Complete the square
coefficient of the x term: 10
divide coefficient in half: 5
square it: 5²
use 5² to complete the square and keep the equation balanced:
-32+2·5² = 2(x² + 10x + 5²)
18 =2(x+5)²
9 = (x+5)²
x+5 = ±√9 = ±3
x = ±3 - 5 = -2, -8
A pet shelter had fifty -four puppies and another six weee brought in. If ten puppies a day were adopted, how long would it take for all of them to be adopted?
Answer: 6 weeks
6 weeks
Step-by-step explanation:
666
mark is a carpenter he is trying to decide how much money to charge for his next job to do the job he will need to buy supplies that will cost $275 he will also need to rent a machine that will cost $125 he wants to charge enough to have $150 profit how much money should mark charge for the job
Question 13
Find the value of each variable so that the quadrilateral is a parallelogram.
Ey+3
15
4
H
X =
y =
Answer:
x-3=15
x=18
y+3=12
y=9...........
To which set or sets of numbers does the number 5 belong?
Group of answer choices
A) rational numbers only
B) integers only
C) integers and rational numbers only
D) integers, whole numbers, and rational numbers
Answer:
D.
Step-by-step explanation:
A 2-year old mice can solve a simple maze in 30 seconds on average, with a standard deviation of 2 seconds. In a recent experiment, a group of 25 2-year old mice were given the blood of younger mice to see if there is any improvement in terms of cognitive functions. These mice were observed to solve the same maze in 29 seconds. Can we say that the blood transfusion improved the cognitive functions of 2-year old mice (i.e. shorter time to solve the maze)?
Required:
a. State the hypotheses.
b. What is the p-value?
c. Using α = 0.05, what is your conclusion?
Answer:
a)
Null Hypothesis H₀ : μ = 30
Alternative Hypothesis H₁ : μ < 30
b)
p-value = 0.0099
c)
Since 0.0099 < 0.05
Therefore, there is enough evidence to conclude that blood transfusion improved the cognitive functions of 2-year old mice.
Step-by-step explanation:
Given the data in the question,
a) State the hypotheses.
Null Hypothesis H₀ : μ = 30
Alternative Hypothesis H₁ : μ < 30
b) What is the p-value
Test statistics
t = ([tex]x^{bar}[/tex] - μ) / s/√n
t = (29 - 30) / (2/√25)
t = -1 / 0.4
t = -2.5
degree of freedom df = n-1 = 25 - 1 = 24
from table
p-value = 0.0099
c) Using α = 0.05, what is your conclusion?
p-value = 0.0099
α = 0.05
0.0099 < 0.05
So, there is enough evidence to conclude that blood transfusion improved the cognitive functions of 2-year old mice.
There are 48 students going on a field trip and 1/4 are girls how many boys are going on the field trip? In tape diagram
Answer:
3/4 or 75% are boys
Step-by-step explanation:
please help me with these problems. This is not multiple choice. Part 3
9514 1404 393
Answer:
5. 8 ft
6. y = 47x +110; 533 students in 2019
Step-by-step explanation:
4. Answered for you previously. See https://brainly.com/question/21087377.
__
5.
Given:
triangular garden with base 7 ft and area 28 ft^2
Find:
height of the triangle
Solution:
The formula for the area of a triangle is ...
A = 1/2bh . . . . . where A is the area, b is the base length, and h is the height
Multiplying by 2/b, we can get a formula for the height. Using this formula, we can solve the problem.
h = 2A/b
We can let h represent the height, and fill in the given data.
h = 2(28 ft^2)/(7 ft)
h = 8 ft
The height of the triangle is 8 feet.
__
6.
Given:
(0, 110), (5, 345) . . . . . where the points represent ...
(years after 2010, students using the hotline)
Find:
a linear model for the data
the number of students predicted for 2019
Solution:
The 2-point form of the equation for a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
where the points are (x1, y1) and (x2, y2). Using the given points, our linear model is ...
y = (345 -110)/(5 -0)(x -0) +110
y = 47x +110 . . . . the linear model, where ...
y is the number of students using the hotline
x is the number of years after 2010
__
In 2019, x = 9, so y = ...
y = 47(9) +110 = 423 +110 = 533
The number of students predicted to use the hotline in 2019 is 533.
Answer:
Q4. 2.5 milesQ5. 8 ftQ6. 533 studentsStep-by-step explanation:
Q4
Tom's speed upstream would be:
8 - 3 = 5 mph as he is moving against the currentThe distance traveled in 30 min:
30 min = 1/2 h5 mph*1/2 h = 2.5 milesQ5
Triangle area formula:
A = 1/2bhA and b given, substitute values to find the value of h:
28 = 1/2*7hh = 28*2/7h = 8 ftQ6
Change in number of students over 5 years:
345 - 110 = 235Rate of change per year:
235/5 = 47Predicted number of students in 2019
345 + 47*(2019 - 2015) = 345 + 47*4 = 533 studentsWho ever gets it right gets brainliest
Answer:
Tuba, French Horn, Trombone, Trumpet, Cornet.
Someone Find the area of a triangle with the height of 11 inches and a base of 5 inches
Answer:
27.5 inches
Step-by-step explanation:
A= 1/2bh
A= 1/2(5)(11)
A=1/2(55)
A= 27.5
9
Subtract the following polynomials: *
(1 Point)
(4x2 - 17x3 + 9) - (x² + 9x + 23x² + 11)
0 - 19.73 – 25x2 – 12x – 3
- 10.x3 – 162x2 – 24x - 4
-17x3 - 20x2 – 9x 2
-16x3 – 243x2 – 12x – 3
Step-by-step explanation:
1) Your problem → (4x^2 - 17x^3 + 9) - (x^2 + 9x + 23x^2 + 11)
(-17x^3+4x^2+9)-(x^2+23x^2+9x+11)
=-17x^3+4x^2+9-x^2-23x^2-9x-11
=-17x^3+4x^2-x^2-23x^2-9x+9-11
=-17x^3-20x^2-9x-2
2) Your problem → 0 - 19.73 - 25x^2 - 12x - 3
=0-19.73-25x2-12x-3
=-25x^2-12x-22.73
3) - 10.x^3 – 162x^2 – 24x - 4
4) Your problem → 17x^3 - 20x^2 - 9x^2
=17x^3-20x^2-9x^2
=17x^3-29x^2
5) -16x^3 – 243x^2 – 12x – 3
A snowmaking machine makes 3/4 inch of snow each minute. How many inches of snow can the machine make in 8 minutes?
Answer:
Step-by-step explanation:
8 minutes × (¾ inch)/minute = 8×¾ inches = 6 inches
Evaluate the expression
15
X - 6, when x= 4.
es
Answer:
54
Step-by-step explanation:
I'm assuming the equation looks like this: 15x - 6
15*4 - 6
60 - 6
54
OR if it's just x-6 then the answer is -2
Hope this is what you were asking, have a nice day! :)
Suiting at 6 a.m., cars, buses, and motorcycles arrive at a highway loll booth according to independent Poisson processes. Cars arrive about once every 5 minutes. Buses arrive about once every 10 minutes. Motorcycles arrive about once every 30 minutes.
(a) Find the probability that in the first 20 minutes, exactly three vehicles-two cars and one motorcycle-arrive at the booth.
(b) At the toll booth, the chance that a driver has exact change is 1/4. independent of vehicle. Find the probability that no vehicle has exact change in the first 10 minutes.
(c) Find the probability that the .seventh motorcycle arrives within 45 minutes of the third motorcycle.
(d) Find the probability that at least one other vehicle arrives at the toll booth between the third and fourth car arrival.
Answer:
Step-by-step explanation:
From the information given:
the rate of the cars = [tex]\dfrac{1}{5} \ car / min = 0.2 \ car /min[/tex]
the rate of the buses = [tex]\dfrac{1}{10} \ bus / min = 0.1 \ bus /min[/tex]
the rate of motorcycle = [tex]\dfrac{1}{30} \ motorcycle / min = 0.0333 \ motorcycle /min[/tex]
The probability of any event at a given time t can be expressed as:
[tex]P(event \ (x) \ in \ time \ (t)\ min) = \dfrac{e^{-rate \times t}\times (rate \times t)^x}{x!}[/tex]
∴
(a)
[tex]P(2 \ car \ in \ 20 \ min) = \dfrac{e^{-0.20\times 20}\times (0.2 \times 20)^2}{2!}[/tex]
[tex]P(2 \ car \ in \ 20 \ min) =0.1465[/tex]
[tex]P ( 1 \ motorcycle \ in \ 20 \ min) = \dfrac{e^{-0.0333\times 20}\times (0.0333 \times 20)^1}{1!}[/tex]
[tex]P ( 1 \ motorcycle \ in \ 20 \ min) = 0.3422[/tex]
[tex]P ( 0 \ buses \ in \ 20 \ min) = \dfrac{e^{-0.1\times 20}\times (0.1 \times 20)^0}{0!}[/tex]
[tex]P ( 0 \ buses \ in \ 20 \ min) = 0.1353[/tex]
Thus;
P(exactly 2 cars, 1 motorcycle in 20 minutes) = 0.1465 × 0.3422 × 0.1353
P(exactly 2 cars, 1 motorcycle in 20 minutes) = 0.0068
(b)
the rate of the total vehicles = 0.2 + 0.1 + 0.0333 = 0.3333
the rate of vehicles with exact change = rate of total vehicles × P(exact change)
[tex]= 0.3333 \times \dfrac{1}{4}[/tex]
= 0.0833
∴
[tex]P(zero \ exact \ change \ in \ 10 minutes) = \dfrac{e^{-0.0833\times 10}\times (0.0833 \times 10)^0}{0!}[/tex]
P(zero exact change in 10 minutes) = 0.4347
c)
The probability of the 7th motorcycle after the arrival of the third motorcycle is:
[tex]P( 4 \ motorcyles \ in \ 45 \ minutes) =\dfrac{e^{-0.0333\times 45}\times (0.0333 \times 45)^4}{4!}[/tex]
[tex]P( 4 \ motorcyles \ in \ 45 \ minutes) =0.0469[/tex]
Thus; the probability of the 7th motorcycle after the arrival of the third one is = 0.0469
d)
P(at least one other vehicle arrives between 3rd and 4th car arrival)
= 1 - P(no other vehicle arrives between 3rd and 4th car arrival)
The 3rd car arrives at 15 minutes
The 4th car arrives at 20 minutes
The interval between the two = 5 minutes
For Bus:
P(no other vehicle other vehicle arrives within 5 minutes is)
= [tex]\dfrac{6}{12} = 0.5[/tex]
For motorcycle:
[tex]= \dfrac{2 }{12} = \dfrac{1 }{6}[/tex]
∴
The required probability = [tex]1 - \Bigg ( \dfrac{e^{-0.5 \times 0.5^0}}{0!} \times \dfrac{e^{-1/6}\times (1/6)^0}{0!} \Bigg)[/tex]
= 1- 0.5134
= 0.4866
“please help me! I will mark you brainly”
Answer:
Here!!
Step-by-step explanation:
It has been hypothesized that overall academic success for college freshmen as measured by grade point average is a function of IQ scores (X1) hours spent studying each week (X2), and one's high school average (x3). Suppose the regression equation is Y (this is Y hat)=6.9+0.055x1 (the 1 is subscripted)+0.107x2 ( the 2 is subscripted)+0.0853X3 (the 3 is subscripted). The multiple standard error is 6.313 and R^2=0.826.
A. What is the predicted GPA for a student with a IQ of 108, 32 hours spent studying per week and a high school average of 82?
B. Which independent variable has the smallest affect on GPA?
C. For which independent variable does a unit change have the greatest effect on the GPA?
Answer:
23.2586 ; IQ ; hours spent studying per week
Step-by-step explanation:
Given the regression model:
y = 6.9+0.055x1 +0.107x2 + 0.0853X3.
IQ scores = (X1)
Hours spent studying each week = (X2),
one's high school average = (x3)
The multiple standard error is 6.313 and R^2=0.826.
What is the predicted GPA for a student with a IQ of 108, 32 hours spent studying per week and a high school average of 82?
X1 = 108 ; X2 = 32 ; X3 = 82
y = 6.9 + 0.055(108) + 0.107(32) + 0.0853(82)
y = 23.2586
B.
The Independent variable with the smallest effect on GPA is the variable with the smallest Coefficient, which is IQ with a Coefficient of 0.055
C.
The Independent variable whiae unit change has the greatest effect on GPA is X2, hours spent studying per week as it has the highest Coefficient of all independent variables with a Coefficient value of 0.107.
Depending on a given set of conditions and the properties of triangles, any of these four outcomes is possible when constructing triangles:
No triangles fit the condition.
One unique triangle fits the condition.
Two triangles fit the condition.
Infinitely many triangles fit the condition.
Complete the steps below to find the number of triangles that can be constructed based on the following conditions: one side measures 7 centimeters, another side measures 9 centimeters, and the angle between them measures 74°.
Part A
What does the dotted line in the diagram represent?
Part B
Now think about changing the triangle. What happens to angle Z if the unknown side length increases while keeping the known side lengths (XZ and ZY) the same? Will the triangle still fit the given conditions?
Part C
What happens to angle Z if the unknown side length decreases while keeping the known side lengths (XZ and YZ) the same? Will the triangle still fit the given conditions?
Part D
Based on your conclusions in parts B and C, can the length of the unknown side be changed in any way without changing the given conditions for the triangle?
Part E
You know the given conditions for the triangle are fixed. You also know the unknown side length is fixed. What does this tell you about the two angles adjacent to the unknown side?
Part F
From your conclusions in part E, how many triangles can be constructed based on the given conditions?
Part G
Let c be the unknown side of the triangle. Use this triangle calculator to solve for c. Under Sides, enter 7 for side a and 9 for side b. Under Angles, enter 74 for angle C. Click Calculate once you have entered the information. What is the length of side c?
Part H
Now try to construct a triangle using a different set of measurements. This time, you’ll enter three angle measurements. Return to the Calculator tab, and click the Clear button to begin a new calculation.
Under Angles, enter 45 for A, 40 for B, and 95 for C. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given angles.
Part I
Click Clear in the tool to begin a new calculation. This time, you’ll check for valid triangles given two sides and the angle opposite one of the sides.
Under Sides, enter 9 for a and 6 for b. Under Angles, enter 30 for B. Then click Calculate. What happened? What message did the tool deliver? Click “Show other solution” in the tool and explain the message in terms of the angle measurements and the given information.
Part J
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given two angles and the side between them.
Under Sides, enter 5 for a. Under Angles, enter 30 for B and 50 for C. Then click Calculate. How many triangles can be created from the given conditions?
Part K
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given three sides of specified length.
Under Sides, enter 6 for a, 7 for b, and 13 for c. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given side lengths.
Answer:
Part A
the dotted line formes the thrid side of the triangle.
part B
The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.
part c
If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.
part D
You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.
part e
The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.
part f
Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters
Answer:
The tool gave a message that read, “The specified values do not match a valid triangle.” That is because the sum of the lengths of two sides of a triangle must be greater than the length of the third side. In this case, the sum is equal to the third side, not greater than the third side:
7 + 6 = 13. No triangles can be constructed with the given conditions.
Step-by-step explanation:
Here is the Edmentum sample answer so I would change it up a little bit!
Have a good day :)
Simplify the expression. (3.5x - 5) + (7.2x + 10)
Answer: 10.7x + 5
Step-by-step explanation:
(3.5 + 7.2)x + (-5 + 10) = 10.7x + 5
PLSSSSS HELP AS SOON AS POSSIBLE <3 Perform the Indicated operation.
6/8 - 3/8
1/8
5/8
3/8
1 1/8
Answer:
3/8
Step-by-step explanation:
6/8 - 3/8 = 3/8
You will get this answer if you type it in a calculator.
In which relationship is the constant of proportionality 1/3?
. Write 3.476 x 1011 in standard notation.
Answer: 347,600,000,000
Step-by-step explanation: You have to move the decimal 11 places. After you move it behind the 6 to get the number 3,476, you have to move it 8 more times because 11-3 is 8. So you add 8 zeros
Which point is collinear to points A and D?
B
D
A. B
B. C
F
C. E
E
D. F
Answer:
D) F
Step-by-step explanation:
HELPPPP ME PLEASEEEEEE
Cal is creating a circular garden for his yard. The radius of the garden is 15 feet. He wants to put fencing around the garden that costs $3.54 per foot. How much will the fencing cost?
The circumference of the garden in feet is ??? feet (DO NOT ROUND)
Using the circumference, the cost of the fencing will be $ ??? (ROUND TO NEAREST CENT)
Answer: 53.10 thing so
Step-by-step explanation:
Evaluate the expression:
Based on the clues in this excerpt, what will most likely happen next?
A. The neighbors will become suspicious of Woman One.
B. The neighbors will apologize to Goodman and leave.
C. The neighbors will get their electricity back.
D. The neighbors will remain suspicious of Goodman.
Answer:
D. The neighbors will remain suspicious of Goodman
Explanation:
He still can't explain anything + I took the test :)
by CODY
The neighbors will start to believe that Les Goodman is an alien.
Option (D) is correct.
It is to find will most likely happen next?
What is most likely event?More Likely (More Probable) One event (A) is more likely to occur than another event (B) when the theoretical probability of the event (A) is greater then that of the other event (B).
This excerpt is from the play the Monsters Are Due on Maple Street.
In this play, the people become suspicious of less Godman as they observe some unusual activities in the town.
They start gossiping about the roar of sound and a flash of light that took place at midnight.
The people of the town got scared but they heard nothing when they turned their radios on.
so, the neighbors will start to believe that Les Goodman is an alien.
Learn more about most likely event here:
https://brainly.com/question/20431230
#SPJ5
Convert 150 to radian measure in terms of p
Answer:
2.618 radians
Step-by-step explanation:
Problem Solve 88 – (–35)
While taking inventory if his pastry shop Noah realize that he had 4 7/8 boxes of baking powder yesterday but the supply is now down to the 1/2 of a box how much more baking powder did Noah have yesterday?
Answer:
4 3/8
Step-by-step explanation:
4 and 7/8 - 1/2 = 4 and 7/8 - 4/8 = 4 and 3/8 of a box more
( 2u + 8) + ( 15u + 7)
Answer:
17u+15
Step-by-step explanation: 15u+2u=17u add 8+7=15
Answer:
17u+15
Step-by-step explanation:
2u+15u+7+8
17u+15
You'd like to purchase a new car when you graduate and start working. The car that you would really like costs $38,000. You've
checked with the bank and based on your income, you would qualify for a car loan with an annual interest rate of 4.32% with a 5-
year repayment period. You now realize that you're not able to afford this car payment each month and still pay your other monthly
expenses. The bank offers a 7-year car loan with the same interest rate. If you were to choose the 7-year car loan instead of the 5-
year car loan, how much lower would your monthly payment be? (Round answer to nearest whole number)
Answer:
174.23 lower p/month
Step-by-step explanation:
7 yr car loan = 38000 x 1.0432^7 =51092.4402043 =$51092.44 total pay back
51092.4402043/84=608.243335765 =$608.24
5 yr car loan = 38000 x 1.0432^5=46948.4748551 =$46948.48 total pay back
46948.4748551/60 =782.474580918 = 782.48 p/month
Amount difference
782.474580918-608.243335765 =174.231245153 =$174.23
For 7 year car loan, the monthly payment will be $180.96 lower as compare to 5 year car loan.
Simple Interest :The simple interest is computed as,
[tex]A=\frac{P*R*T}{100}[/tex]
Where P is principle, R is rate and T is time.
Given that, cost of car [tex]P=38000,R=4.32,T=5years[/tex]
Substitute values in above equation.
[tex]A=\frac{38000*4.32*5}{100} =8208[/tex]
The amount paid in 5 years[tex]=38000+8208=46208[/tex]
Amount paid per month is, [tex]=\frac{46208}{60}=770.14[/tex]
For 7 years,
[tex]A=\frac{38000*4.32*7}{100}=11491.2[/tex]
Amount paid per month is,[tex]=\frac{49491.2}{84}=589.18[/tex]
The Amount difference is, [tex]=770.14-589.18=180.96[/tex]
For 7 year car loan, the monthly payment will be $180.96 lower as compare to 5 year car loan.
Learn more about the Simple interest here:
https://brainly.com/question/20690803
