Use the piecewise function below to evaluate the points f(–3), f(0), and f(–1).
{9x,x−4,x<−1x≥−1
Question 17 options:
f(–3) = –7, f(0) = –0, and f(–1) = 5
f(–3) = –27, f(0) = –4, and f(–1) = 5
f(–3) = –7, f(0) = –4, and f(–1) = –1
f(–3) = –27, f(0) = –4, and f(–1) = –5
Given:
The piecewise function is:
[tex]f(x)=\begin{cases}9x & \text{ if } x<-1 \\ x-4 & \text{ if } x\geq -1 \end{cases}[/tex]
To find:
The values of [tex]f(-3),f(0), f(-1)[/tex].
Solution:
In the given piecewise function,
[tex]f(x)=9x[/tex] for [tex]x<-1[/tex] and [tex]f(x)=x-4[/tex] for [tex]x\geq -1[/tex].
Putting [tex]x=-3[/tex] in [tex]f(x)=9x[/tex], we get
[tex]f(-3)=9(-3)[/tex]
[tex]f(-3)=27[/tex]
Putting [tex]x=0[/tex] in [tex]f(x)=x-4[/tex], we get
[tex]f(0)=0-4[/tex]
[tex]f(0)=-4[/tex]
Putting [tex]x=-1[/tex] in [tex]f(x)=x-4[/tex], we get
[tex]f(-1)=-1-4[/tex]
[tex]f(-1)=-5[/tex]
The required values are [tex]f(-3)=27,f(0)=-4,f(-1)=-5[/tex].
Therefore, the correct option is D.
ASAP!!! Use the relationships in the diagrams below to calculate the the values of the variables if possible part. B
Answer: y = 57°;
Angle Values: 66° and 114°.
Step-by-step explanation:
The sum of the corresponding angles is 180°.
y + 9 + 2y = 180
3y = 180 - 9
3y = 171
y = 57
Angle Values:
57° + 9° = 66°
57° · 2 = 114°
How many times bigger is a group of 20 coins than a group of 5 coins
Answer:
It is there difference:
20-5
15
The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the product will last can be described by a normal distribution. In particular, the average waffle iron lasts for 12 years and one standard deviation is 8 months. How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time
Answer:
They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average waffle iron lasts for 12 years and one standard deviation is 8 months.
Measuring the time in months, we have that [tex]\mu = 12*8 = 96[/tex] and [tex]\sigma = 8[/tex]
How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time?
This is X when Z has a p-value of 0.067, so X when Z = -1.5. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.5 = \frac{X - 96}{8}[/tex]
[tex]X - 96 = -1.5*8[/tex]
[tex]X = 84[/tex]
84 months = 7 years.
They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.
DIC A student has a total of $3000 in student loans that will be paid with a 48-month installment loan with monthly payments of $73.94. Determine the APR of the loan to the nearest one-half of a percent
Answer:
The APR of the loan was 18.30%.
Step-by-step explanation:
Given that a student has a total of $ 3000 in student loans that will be paid with a 48-month installment loan with monthly payments of $ 73.94, to determine the APR of the loan to the nearest one-half of a percent the following calculation must be done:
3,000 = 100
(73.94 x 48) = X
3,000 = 100
3,549.12 = X
3,549.12 x 100 / 3,000 = X
354,912 / 3000 = X
118.30 = X
118.30 - 100 = 18.30
Therefore, the APR of the loan was 18.30%.
cort
Here are ten numbers:
3 7 2 4 7 5 7 1 8 8
Write down the mode.
b)
Work out the median.
c)
Calculate the mean.
What is the range?
Answer:
The mode is 7 and 8
The mean is 5.2
The range is 7
solve the equation
[tex] \frac{1}{6 - d} = \frac{1}{d - 5} [/tex]
Answer:
5.5
Step-by-step explanation:
[tex] \frac{1}{6 - d} = \frac{1}{d - 5} \\ \\ \therefore \: 6 - d = d - 5 \\ \\ 6 + 5 = d + d \\ \\ 11 = 2d \\ \\ d = \frac{11}{2} \\ \\ d = 5.5[/tex]
Please helpppppppppppp
Answer:
It takes _8_ s for an object to fall 1000 feet. In 10 s, an object will fall _1600_ feet.
Step-by-step explanation:
A. Determination of the time it takes for the object to 1000 ft.
Distance (d) = 1000 ft
Time (t) =?
t = √(d/16)
t = √(1000/16)
t = 8 s
B. Determination of how much feet an object will fall in 10 s.
Time (t) = 10 s
Distance (d) =?
t = √(d/16)
10 = √(d/16)
Take the square of both side
10² = d/16
100 = d/16
Cross multiply
d = 100 × 16
d = 1600 ft
SUMMARY
It takes _8_ s for an object to fall 1000 feet. In 10 s, an object will fall _1600_ feet.
In AUVW, W = 840 cm, u = 350 cm and ZV=63º. Find the area of AUVW, to the
nearest square centimeter.
Answer:
[tex]Area = 130977cm^2[/tex]
Step-by-step explanation:
Given
[tex]W=840[/tex]
[tex]U = 350[/tex]
[tex]\angle V = 63^o[/tex]
Required
The area
The area is calculated as:
[tex]Area = \frac{1}{2}UW\sin(V)[/tex]
So, we have:
[tex]Area = \frac{1}{2}*350*840*\sin(63^o)[/tex]
[tex]Area = \frac{1}{2}*350*840*0.8910[/tex]
[tex]Area = 130977cm^2[/tex]
what is 7x+3y=9 in y-intercept form?
Answer:
y = -2 1/3+3
Step-by-step explanation:
-Subtract 7x from each side of equation
-divide by 3 on each side
7x+3y = 9
3y = -7x+9
y = -7/3+3
:) ur welcome
If f(x) = 3x⁴ - 13x, find f(-2)
Answer:
answer is
74....................
What is the first step in using the square root property?
Answer: Isolate the term that contains the squared variable. Then, take the square root of both sides and solve.
Step-by-step explanation:
To solve an equation by using the square root property, you will first isolate the term that contains the squared variable. You can then take the square root of both sides and solve for the variable. Make sure to write the final answer in simplified form.
Cos15°°- Sin 15°= 1/√2
Hope it's help you
All of the following statements have the same value except..?
1. six below zero
2. the opposite of six
3. negative six
4. the absolute value of six
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
Let's consider each of the statements.
1. Six below zero.
⟹ Any number below zero will be negative. So, the value will be [tex]\boxed{-6}[/tex]
____________________
2. The opposite of six.
⟹ The opposite of 6 wil be negative 6. The value again will be [tex]\boxed{-6}[/tex]
____________________
3. Negative six.
⟹ Negative six in numerical form is [tex]\boxed{-6}[/tex]
____________________
4. The absolute value of six.
⟹ Here they've asked the absolute value of 6 which will be [tex]\boxed{6}[/tex]
____________________
⏩ So, the statement which doesn't have the same value will be ⇻ [tex]\boxed{statement \ 4}[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex]RainbowSalt2^{2}2^{2}[/tex]
determine the general term of this sequence 2;10;18;26;.........;394
Answer:
Tn=8n-6
Step-by-step explanation:
this is arithmetic sequence so first we check our difference by saying
T2-T1=T3-T2
10-2=18-10
so difference =8 nd a=2
Formula for arithmetic is Tn=a + (n-1)d
then substitute Tn=2 + (n-1)(8)
Tn=2 + 8n-8
Tn=8n-6
1. There are 2 schools. Each school has 3 buildings. Each building has 4 floors. Each floor has 5 classrooms. Each classroom has 6 rows of desks. Each row has 7 desks. How many desks are there in the two schools?
Which expression represents the area in square centimeters of the new cup opening? Use A=2
Answer:
A = πx² - 2πx + π
Step-by-step explanation:
The area of the new cup opening :
We are given the area formula to use :
Area, A = πr²
r = Radius = x-1
Area = π(x - 1)²
A = π(x - 1)(x - 1)
A = π(x² - x - x + 1)
A =π(x² - 2x + 1)
A = πx² - 2πx + π
Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price per comic?
$ per comic?
Answer:
$0.25
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Which two graphs can be combined to represent 140% HELP PLEASE
Answer:
Step-by-step explanation:
Since all the grids have 100 squares, which grid has all squares shaded? And which grid has 40 (4 columns) shaded? This add up to 100+40=140. The answer, of course, is C+D (last answer). None of the others have enough shaded squares
sammy is on level 40 , which is five times as much as rocky.what islevel rocky on
Answer:
8
Step-by-step explanation:
40÷5=8
Hope this helps! :)
100 Brainly points!!!!
In the figure, polygon ABCD is dilated by a factor of 2 to produce A’B’C’D’ with the origin as the center of dilation.
Point A’ is at _ options > •(2,1), (-2,-2), (1,2), (-2,2)•
& point D is at _ options > (-2,2), (4,-2), (4,2), (-2,-2).
Answer:
Point A’ is at (-2,-2)
& point D' is at (4,-2)
Step-by-step explanation:
Point A’ => (-1×2, -1×2) => (-2 , -2)
Point D' => (2×2 , -1×2) => (4 , -2)
A is at (-1,-1)
So A' is at
2(-1,-1)(-2,-2)D is at
(2,-1)D' is at.
2(2,-1)(4,-2)Hallar la ecuación de la recta (2,3) y (1,-2)
Answer:
[tex]y=5x-7[/tex]
Step-by-step explanation:
can you do 3 pages of work for me?
Answer:
if it is easy i can do it
hope it helps
Answer:
3
Step-by-step explanation:
I will help
A workbench for a motorcycle is in the shape of parallelogram IJKL. The motorcycle is
raised and lowered as the angles of the parallelogram change. Which statement is
correct?
ZJ and ZL are supplementary
ZJ and ZK are congruent.
65° K
ZJ and ZK are supplementary
ZI and ZL are congruent.
Answer:
J and K are supplementary
Step-by-step explanation:
Given
The attached image
Required
The true statement
From the attached image, it is hard to determine the values of angles I and L as there are no enough information to determine their values.
However, J and K can be worked easily.
From the image
[tex]J = 65^o[/tex] --- vertically opposite angles
And:
[tex]K + 65^o = 180^o[/tex] ---- angle on a straight line
Substitute: [tex]J = 65^o[/tex]
[tex]K + J = 180^o[/tex]
When two angles add up to 180, the angles are supplementary.
Hence, (c) is correct
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 590(1.79)
Answer:
growth
79% rate of increase
Step-by-step explanation:
1.79 is > than 1
therefor growth
1.79 = 79% rate of increase
Tính I = tích phân ( x^2 - 3xy) dx + ( x-y) dy với đường cung định hướng AB là ve tẻ nối điểm A ( 2,3 ) và B ( 1 , 1 )
1. Of the three angles in a right-angled triangle, one angle has a measure
of 60 degrees. What is the measure of the third angle, Angle X? *
al 60
Answer:
30. A right triangle has one angle that is 90°
All angles add to 180°
180 - 90 - 60 = 30
Step-by-step explanation:
Debbie did a survey of how many states the members of her class had visited. The results were: 10, 15, 23, 2, 21, 31, 14, 10,
8.17, 11, 19.8.42.15. 22. 6, 34, 19.3, 24,
What is the five-number summary for this set of data?
Answer:
Step-by-step explanation:
11 22 6 34 19
Charlie weighed 8 lbs. 11 oz. at birth given that 1 pound is equivalent to 16 ounces what is Charlie’s birthweight expressed in ounces
Answer:
139 oz.
Step-by-step explanation:
If 1 pound equals 16 ounces, multiply 8 by 16 and you will get 128, then add the original 11 ounces to get 139.
3(t+4)=9 t=?
-(c-6)=0 c=?
-10(s+4)=-122 s=?
Answer:
t = -1
c = 6
s = 8.2 or 8 1/5 (same thing just different notation)
Step-by-step explanation:
3(t+4) = 9
3t + 12 = 9
3t = -3
t = -1
-(c-6) = 0
-c + 6 = 0
-c = -6
c = 6
-10(s+4) = -122
-10s - 40 = -122
-10s = -82
10s = 82
s = 82/10 = 8.2 or 8 2/10 or 8 1/5
