Answer:
f(x) = 16*0.75^x
Step-by-step explanation:
first off let's use this coordinate (the one given) :
(0,16)
let's substitute this into the equation with x being 0 and f(x) being 16
16 = a*b^0
*anything to the power of 0 is 1*
so:
a = 16
now use the second coordinate :
(1,12)
and do the same by substituting 1 for x and 12 for f(x), we also know what 'a' is:
12 = 16*b^1
12 = 16 * b
b = 3/4
so :
f(x) = 16*0.75^x
Answer:
f(x) = 16(.75)^x
Step-by-step explanation:
Find the value(s) of a in the domian of f for which f(a)=1.
f (x)=x^2+2x-2
Answer:
1 ≤ y < ∞
Step-by-step explanation:
very true
My question is very simple and yes I'm saying all this bc I can't ask without 20 words- What is 400 cubed?
Answer: 64000000
Explanation: Why are you named as my ALT-
The entire graph of the function f is shown in the figure below.
Write the domain and range of f using interval notation.
Answer:
below
Step-by-step explanation:
domain. = ( -5 , 4)
range = ( -2 , 3)
Use the Laplace transform to solve the given system of differential equations.
Let X(s) and Y(s) denote the Laplace transforms of x(t) and y(t), respectively. Then taking the transform of both sides of both equations gives
LT[dx/dt + 5x + dy/dt] = LT[1]
==> s X(s) - x (0) + 5 X(s) + s Y(s) - y (0) = 1/s
==> s X(s) + 5 X(s) + s Y(s) = 1/s
==> (s + 5) X(s) + s Y(s) = 1/s
LT[dx/dt - x + dy/dt - y] = LT[exp(t )]
==> s X(s) - x (0) - X(s) + s Y(s) - y (0) - Y(s) = 1/(s - 1)
==> s X(s) - X(s) + s Y(s) - Y(s) = 1/(s - 1)
==> (s - 1) X(s) + (s - 1) Y(s) = 1/(s - 1)
Solve for X(s) and Y(s). Using elimination, you would get
X(s) = (1 - 2s) / (5s (s - 1)²)
Y(s) = (7s - 1) / (5s (s - 1)²)
Now take the inverse transforms of each. Start by getting the partial fraction decompositions:
(1 - 2s) / (5s (s - 1)²) = 1/5 (a/s + b/(s - 1) + c/(s - 1)²)
-2s + 1 = a (s - 1)² + bs (s - 1) + cs
-2s + 1 = (a + b) s ² + (-2a - b + c) s + a
==> a + b = 0, -2a - b + c = -10, a = 5
==> a = 1, b = -1, c = -1
==> X(s) = 1/5 (1/s - 1/(s - 1) - 1/(s - 1)²)
Similarly, you would find
Y(s) = -1/5 (1/s - 1/(s - 1) - 6/(s - 1)²)
Now for the inverse transforms:
LT⁻¹ [1/s] = 1
LT⁻¹ [1/(s - 1)] = exp(t )
LT⁻¹ [1/(s - 1)²] = t exp(t )
Putting everything together, we have
LT⁻¹ [X(s)] = x(t) = 1/5 - 1/5 exp(t ) - 1/5 t exp(t )
and
LT⁻¹ [Y(s)] = y(t) = -1/5 + 1/5 exp(t ) + 6/5 t exp(t )
PLZZZZZ HURRY WILL GIVE BRAINLIEST!!!!
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds
Yes, because both figures are rectangles and all rectangles are similar.
No, because the center of dilation is not at (0, 0).
No, because corresponding sides have different slopes.
Answer:
option b
Step-by-step explanation:
both are rectangles and similar measures
Yes, because both figures are rectangles and all rectangles are similar
The rectangle EFGH is a result of the dilation of rectangle ABCD
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the first rectangle be represented as ABCD
Now , the rectangle is dilated by a scale factor k
And , the transformed rectangle is given by EFGH
where the center of origin is the scale factor of dilation
Now , the ratios of the sides of the rectangles will be similar
So , the rectangles ABCD and EFGH are similar
Hence , the dilated rectangle is EFGH
To learn more about dilation click :
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The degree of this expression 2x+3y=4
Answer:
1st degree
Step-by-step explanation:
You look at the largest exponet, right here, there are none so it would be 1st degree.
Answer:
1
Step-by-step explanation:
The degree of an expression with multiple exponents is the highest exponent in it. In this expression, there is no expression, so the answer will be 1 because there is no exponent and every variable and number has an invisible 1 as its exponent.
Hope this helps.
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose 26 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants
Answer:
27405
Step-by-step explanation:
There are 6 different variants available for each croissant. There are 26 croissants in all out of which 1 is plain. We use combination and permutation technique to identify different ways to choose croissant.
[5 + 26 - 1 ] 26 = 30C26 = 27405.
For what value of w is4w = 2w - 8
Answer:
w =-4
Step-by-step explanation:
4w = 2w - 8
Subtract 2w from each side
4w-2w = 2w-2w - 8
2w = -8
Divide by 2
2w/2 = -8/2
w = -4
Suppose the shipping weight of your cheese shop's customized gift baskets is asymmetrically distributed with unknown mean and standard deviation. For a sample of 70 orders, the mean weight is 52 ounces and the standard deviation is 8.4 ounces. What is the lower bound of the 99 percent confidence interval for the gift basket's average shipping weight
Answer:
The lower bound of the 99% confidence interval for the gift basket's average shipping weight is of 49.34 ounces.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-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 = 70 - 1 = 69
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 69 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.649
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.649\frac{8.4}{\sqrt{70}} = 2.66[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 52 - 2.66 = 49.34
The lower bound of the 99% confidence interval for the gift basket's average shipping weight is of 49.34 ounces.
How do you do 7-7(-4)
Answer:
35
Step-by-step explanation:
7-7(-4)
Using PEMDAS
Multiply first
7 +28
Then add
35
what it the value of m when (2m+8)° and the other angle 24°
Answer:
m = 74
Step-by-step explanation:
2m+8 +24 has to = 180 because they form a line. So the equation would be 2m+32 = 180, so then 2m would equal 148, so m = 74.
it’s question number 3 and i know the answer but i need someone to explain to me how to get the answer the answer is B. pls can hurry i need the explanation soon
Answer:
2+6=8
Step-by-step explanation:
Start at 2
Then since we are adding 6 move 6 units to the right
I need help please help me
Answer:
Y = (x + 1)^2 - 4
where is
look the Diagram when the line arrow cross to x line got -4 it's mean left side is Negative and reach to y diagram within 1 on positive to below
so the right answer is = Y = (x+1)^2 - 4
What is the next step in solving 0 = x2 + 6x – 10 by completing the square, after you cut 6 in half?
Answer:
see below
Step-by-step explanation:
0 = x^2 + 6x – 10
Add 10 to each side
10 = x^2-6x
Take the coefficient of x
-6
Divide by 2
-6/2 =-3
Square it
(-3)^2 =9
Add 9 to each side
10+9 = x^2-6x+9
We use -3 for the square term
19 = (x-3)^2
Take the square root of each side
±sqrt(19) = x-3
Add 3 to each side
3±sqrt(19) = x
6 Farah is buying clothes from a website.
The website shows this information about a jacket Farah wants to buy.
Jacket
original price £30.99
sale price £16
The website claims this is a saving of 46%.
Is the sale price a saving of 46% on the original price?
Show why you think this.
they
Answer:
No ;
Step-by-step explanation:
Given that :
original price = £30.99
sale price = £16
The percentage saving :
(Original price - sale price) / original price * 100%
(£30.99 - £16) / £30.99 * 100%
£14.99 / £30.99 * 100%
= 0.4837 * 100%
= 48.37%
According to the calculation above, the sale price isn't a saving of 46% on the original price, rather it is a saving of 48.37% on the original price.
Expand & simplify:
(x - 3)(x-4)
Answer:
[tex] {x}^{2} −7x+12[/tex]
Step-by-step explanation:
[tex](x−3)(x−4)[/tex]
[tex]x(x−4)−3(x−4)[/tex]
[tex]x \times x+x(−4)−3x−3(−4)[/tex]
[tex] {x}^{2} −4x−3x+12[/tex]
[tex] {x}^{2} −7x+12[/tex]
Hope it is helpful....Answer:
x
[tex] {x}^{2} - 7x + 12[/tex]
Step-by-step explanation:
[tex](x - 3)(x - 4)[/tex]
[tex]x( x - 4) - 3(x - 4)[/tex]
[tex] {x}^{2} - 4x - 3x + 12[/tex]
[tex] {x}^{2} - 7x + 12[/tex]
What is the answer to
5x9/17+6
Answer:
I don't know which one you mean so I did both:
[tex]\frac{5*9}{17+6} =\frac{45}{23}[/tex] [tex]5*\frac{9}{17} +6=\frac{45}{17} +\frac{102}{17} =\frac{147}{17}[/tex]Simplify 45 - 8 + 12 - (-25)
Answer:
74
Step-by-step explanation:
BODMAS
12-(-25)
=12+25=37
45-8+37
45-8=37
37+37=74
=74
Answer:
37+12+25
74 Answer
hope it helps
John caught a gigantic tuna fish. Every 1/100 of it could fill up a can of tuna fish. How many cans of tuna fish can it make?
Answer:
100
Step-by-step explanation:
if every 1/100 is 1 tuna can you need to multiply the amount of tuna to make a tuna can so it will be 1 so times 100
For the first 6% of Carlene's salary, her employer matches 100% of her 401(k) contributions, and from 6% to 12%, Carlene's employer matches 50% of her 401(k) contributions. Carlene's salary is $40,000, and last year, she contributed $4000 to her 401(k) plan. What was her employer's contribution to the 401(k)?
Carlene's employer's contribution to the 401(k) was of $3,200., using proportions.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is combined with basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
The proportion of her salary that she contributed to the 401(k) plan is of:
4000/40000 = 0.1.
The first 6% of her salary is:
0.06 x 40000 = $2,400.
Hence her employee contributed $2,400 relative to the first 6% of her salary.
For the 4% between 6% and 10%, the employee contributed 50% of her contributions, hence:
0.5 x (4000 - 2400) = 0.5 x 1600 = $800.
Hence the total contribution by the employee is of:
2400 + 800 = $3,200.
More can be learned about proportions at https://brainly.com/question/24372153
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Suppose the national mean annual salary for a school administrator is $91,000 a year. A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state to see if they differed from the national average.
77,600 76,000 90,700 97,200 90,700
101,800 78,700 81,300 84,200 97,600
77,500 75,700 89,400 84,300 78,700
84,600 87,700 103,400 83,800 101,300
94,700 69,200 95,400 61,500 68,800
(a) Formulate hypotheses that can be used to determine whether the population mean annual administrator salary in Ohio differs from the national mean of $91,000.
H0: μ ≤ 91,000
Ha: μ > 91,000
H0: μ > 91,000
Ha: μ ≤ 91,000
H0: μ ≥ 91,000
Ha: μ < 91,000
H0: μ < 91,000
Ha: μ ≥ 91,000
H0: μ = 91,000
Ha: μ ≠ 91,000
(b) The sample data for 25 Ohio administrators is contained in the file named Administrator.
What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)
What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)
p-value =
(c) At
α = 0.05,
can your null hypothesis be rejected? What is your conclusion?
Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Do not reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. Reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Do not reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.
(d) Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses.
H0: μ ≤ 91,000
Ha: μ > 91,000
H0: μ > 91,000
Ha: μ ≤ 91,000
H0: μ ≥ 91,000
Ha: μ < 91,000
H0: μ < 91,000
Ha: μ ≥ 91,000
H0: μ = 91,000
Ha: μ ≠ 91,000
Find the value of the test statistic. (Round your answer to three decimal places.)
State the critical values for the rejection rule. Use
α = 0.05.
(Round your answer to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic≤test statistic≥
State your conclusion.
Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Do not reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary. Reject H0. We cannot conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.Do not reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.
Answer:
H0 : μ = 91000
H1 : μ ≠ 91000
Test statistic = - 2.594
Pvalue = 0.016
|Tcritical | = 2.064
Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.
Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.
Step-by-step explanation:
The hypothesis :
H0 : μ = 91000
H1 : μ ≠ 91000
From the data given :
77600 76000 90700 97200 90700
101800 78700 81300 84200 97600
77500 75700 89400 84300 78700
84600 87700 103400 83800 101300
94700 69200 95400 61500 68800
Using calculator :
Sample mean, xbar = 85272
Sample standard deviation, s = 11039.23
Sample size, n = 25
The test statistic :
(xbar - μ) ÷ (s/√(n))
(85272 - 91000) / (11039.23/√(25)
Test statistic = - 5728 / 2207.846
Test statistic = - 2.594
The Pvalue : df = n - 1 = 25 - 1 = 24
Pvalue(-2.594, 24) = 0.0159
Decision region :
Reject H0 ; If Pvalue < α ;
α = 0.05
Using the critical value :
Decision region :
Reject H0 ; If Test statistic > |Tcritical;
Tcritical value at df = 24 ; α = 0.05 ;
|Tcritical | = 2.064
Hence,
We Reject H0 ; Since, |Test statistic| > |Tcritical|and conclude that mean salary depends differs
simplify expresion 5x³y(2x+3y-4) =
Answer:
5x3 y(5xy-4)
5x3y ×1xy
5x4y2
Answer:
[tex]5 {x}^{3} y[/tex]
step by step
[tex]5 {x}^{3} y(2x + 3y - 4) \\ = 10 {x}^{3}y + 15 {x}^{3} y + 20 {x}^{3} y \\ = 5 {x}^{3} y[/tex]
What is the answercto this equation? 5x+37=-6(1-8×)
Answer:
x=1
Step-by-step explanation:
5x+37=-6(1-8x)
Distribute
5x+37 = -6 +48x
Subtract 5x from each side
5x+37 -5x = -6+48x-5x
37 = -6+43x
Add 6 to each side
37+6 = -6+43x+6
43 = 43x
Divide by 43
43/43 = 43x/43
1 =x
Answer:
x=1
Step-by-step explanation:
5x+37=-6(1-8×)
5x+37=-6(-7)
5x+37=6 x 7
5x+37= 42
5x+37-37=42-37
5x=5
5x/5 = 5/5
x = 1
Hope it Helps !!
3/9 and 5/15 are they equivalent
Answer:
yes
Step-by-step explanation:
3/9 Divide the top and bottom by 3
1/3
5/15 Divide the top and bottom by 5
1/3
They are equal
A man ordered 5 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $ 4.33 per box, and felt-tip pens cost $.3.45 If the man's order of pens totaled $75.30, how many boxes of each type of pen did he buy?
One jar holds 40 purple marbles and 5 black marbles. A second jar holds 90 orange marbles and 10 black marbles. What is the probability that a black marble will be drawn from both jars?
Answer:
1/90Step-by-step explanation:
The first jar holds 45 marbles and 5 of them are black.
The second jar holds 100 marbles and 10 of them are black.
Required probability:
P(b,b) = 5/45*10/100 = 1/9*1/10 = 1/90Now we have to find,
The probability that a black marble will be drawn from both jars.
The given information is,
→ 1st jar contains/holds 45 marbles.
→ 5 of the marbles are black.
→ 2nd jar contains/holds 100 marbles.
→ 10 of the marbles are are black.
Then the probability will be,
→ P(b,b)
→ (5/45) × (10/100)
→ (1/9) × (1/10)
→ 1/90
Thus, required probability is 1/90.
What is the greatest number of acute angles that a triangle can contain?
A.3
B.1
C.0
D.2
Answer:
3
Step-by-step explanation:
We know that the sum of the angles of a triangle is 180
Assume that the angles are equal
x+x+x = 180
3x= 180
x = 180/3 =60
All three angles are less than 90 which makes them acute so we know that we can have 3 acute angles
please help me please help me
14. largest 9510
15. smallest 1000000
16. n+6=22 —> n=22-6 —>n = 16
17. Add : 204 + 38429= 38633
determine the values of X which the sequence
[tex]log3. \: log {3}^{3}. \: log {3}^{x} [/tex]
is (I) arithmetic (II) geometric
Answer:
arithmetic
hyj
bhhm
bm.hg
hgjm
hgjgshmih
mhh
jhuu
Find the dimensions of a rectangle with perimeter 76 m whose area is as large as possible. m (smaller value) m (larger value)
Answer:
19 m
Step-by-step explanation:
Perimeter = 2(length + width) ; P = 2(l+w) - - (1)
Area = Length * width ; A = l*w - - - (2)
76 = 2(l+w)
76/2 = l+w
l+w = 38
l = 38 - w
Put l = 38 - w in (1)
A = (38-w)*w
A = 38w - w²
At maximum point:
dA/dw = 0
dA/dw = 38 - 2w
38 - 2w = 0
38 = 2w
w = 38/2
w = 19