Answer:
36
Step-by-step explanation:
There are 9 different toppings
Pick the first topping
Now there are 8 toppings
Pick the second topping
9*8
72 ways to pick the toppings
But order doesn't matter
pepperoni and hamburger is the same as hamburger and pepperoni, so we divide by 2
72/2 = 36
There are 36 different ways
A square has an area of 50 square feet what is the perimeter of the square rounded to the nearest foot
Answer:
28 feet
Step-by-step explanation:
area of a square = side times side; the sides are equal
50 = side times side or 50 = side^2
sqroot of 50 = sqroot of side^2
7 feet is about the size of the side of the square so using that information..
2 length + 2 width or 4 side
4 times 7 = 28
the perimeter is 28 feet
Subtracting polynomials
Answer:
The other polynomial is 11x^2 -3x
Step-by-step explanation:
12x^2 -5x - ( x^2 -2x) = other polynomial
Distribute the minus sign
12x^2 -5x - x^2 +2x
Combine terms
11x^2 -3x
The other polynomial is 11x^2 -3x
A fitness center is interested in finding a 95% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 246 members were looked at and their mean number of visits per week was 2.2 and the standard deviation was 2.6. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a ? distribution.
b. With 95% confidence the population mean number of visits per week is between and visits.
c. If many groups of 246 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week
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Which of these shows equivalent fractions?
а
=
4.
8
=
AN
alw
10
2 - 3
3. 6
Answer:A
Step-by-step explanation:
a. 2(3y - 2x) = 6y - 4x or rewritten as -4x + 6y
4x + 6y - 8 x
= 4x - 8x + 6y
= -4x + 6y
A ladder is placed 3.5 feet away from the base of a tree. If the ladder forms a 53° angle with the ground, how many feet up the tree will the ladder reach? Write only the number rounded to the nearest tenth of a foot.
Answer:
The ladder will reach 4.6 ft up the tree.
Step-by-step explanation:
When we draw out our triangle, we should see that we are given the horizontal leg and are trying to find the vertical leg. We use tan∅ to help solve:
tan53° = x/3.5
3.5tan53° = x
x = 4.64466
Please help I will mark brainliest for first answer!
Answer:
C.
Step-by-step explanation:
Step 1: Multiply jar weights
12(10) = 120 oz
Step 2: Convert lbs to oz
16 + 14 = 30 oz
Step 3: Add weights
150 oz
Step 4: Convert to lbs
150/16 = 75/8 = 9.375 lbs
9.375 lbs = 9 lbs 6 oz
In the study of a nonlinear spring with periodic forcing, the equation y prime prime plus ky plus ry cubedy′′+ky+ry3equals=Upper A cosine omega tAcosωt arises. Let kequals=44, requals=33, Aequals=77, and omegaωequals=88. Find the first three nonzero terms in the Taylor polynomial approximation to the solution with initial values y(0)equals=0, y prime (0 )y′(0)equals=1.
Answer:
[tex]\mathbf{y(t) = t + \dfrac{7}{2}t^2 - \dfrac{2}{3}t^3+ ...}[/tex]
Step-by-step explanation:
THe interpretation of the given question is as follows:
y'' + ky + ry³ = A cos ωt
Let k = 4, r = 3, A = 7 and ω = 8
The objective is to find the first three non zero terms in the Taylor polynomial approximation to the solution with initial values y(0) = 0 ; y' (0) = 1
SO;
y'' + ky " ry³ = A cos ωt
where;
k = 4, r = 3, A = 7 and ω = 8
y(0) = 0 ; y' (0) = 1
y'' + 4y + 3y³ = 7 cos 8t
y'' = - 4y - 3y³ + 7 cos 8t ---- (1)
∴
y'' (0) = -4y(0) - 3y³(0) + 7 cos (0)
y'' (0) = - 4 × 0 - 3 × 0 + 7
y'' (0) = 7
Differentiating equation (1) with respect to t ; we have:
y''' = - 4y' - 9y² × y¹ - 56 sin 8t
y''' (0) = -4y'(0) - 9y²(0)× y¹ (0) - 56 sin (0)
y''' (0) = - 4 × 1 - 9 × 0 × 1 - 56 × 0
y''' (0) = - 4
Thus; we have :
y(0) = 0 ; y'(0) = 1 ; y'' (0) = 7 ; y'''(0) = -4
Therefore; the Taylor polynomial approximation to the first three nonzero terms is :
[tex]y(t) = y(0) + y'(0) t + y''(0) \dfrac{t^2}{2!} + y'''(0) \dfrac{t^3}{3!}+...[/tex]
[tex]y(t) = 0 + t + 7 \dfrac{t^2}{2!} + \dfrac{-4}{3!} {t^3}+ ...[/tex]
[tex]\mathbf{y(t) = t + \dfrac{7}{2}t^2 - \dfrac{2}{3}t^3+ ...}[/tex]
6.1.3
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
Answer:
The requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.
Step-by-step explanation:
A normal-distribution is an accurate symmetric-distribution of experimental data-values.
If we create a histogram on data-values that are normally distributed, the figure of columns form a symmetrical bell shape.
If X [tex]\sim[/tex] N (µ, σ²), then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Thus, the requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.
Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 156 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?
Answer:
140608 cubic in
Step-by-step explanation:
[tex]x+x+h=156[/tex]
[tex]h=156-2 x[/tex]
[tex]V=x^{2} h \quad[/tex] We eliminate one of the variables
[tex]V=x^{2}(156-2 x)[/tex]
[tex]V=156 x^{2}-2 x^{3}[/tex] Differentiating [tex]v[/tex]
[tex]V^{\prime}=312x-6 x^{2} \quad[tex] When [/tex]V=0[/tex]
[tex]312x-6 x^{2}=0[/tex]
[tex]x(312-6 x)=0 \quad=\quad\left\{\begin{array}{l}x=0 \\ x=52 \quad x=0 \text { not acceptable }\end{array}\right.[/tex]
[tex]h=156-2(52)=\Rightarrow h=52[/tex]
[tex]V=52\times52\times52= 140608 \text{ cubic in}[/tex]
When the factors of a trinomial are (x + p) and (x + 9) then the constant term
of the trinomial is:
Answer:
9p
Step-by-step explanation:
(x + p)(x + 9) =
= x^2 + 9x + px + 9p
= x^2 + (9 + p)x + 9p
The constant term is 9p.
Please help with how to find the area of the shape with work
Answer: 10 squares.
Step-by-step explanation:
We can do it with integrals.
If we take the bottom vertex as the point (0,0), the top right vertex as the point (0,4) and the left vertex as the point (5, 6)
then the area of the triangle is the area enclosed by two lines between the values x = 0 and x = 5.
the two lines are:
the bottom is the one that passes through (0,0) and (5,6)
f(x) = y = s*x (because it passes through the point (0,0))
and the slope is s = 6/5.
so f(x) = y = (6/5)*x.
The top line is the one that passes through (0,4) and (5,6)
the y-intercept is b = 4, and the slope is:
s = (6 - 4)/(5 - 0) = 2/5.
g(x) = y = (2/5)*x + 4.
Now, the area enclosed for the triangle is equal to:
[tex]\int\limits^5_0 {g(x) - f(x)} \, dx[/tex]
this is equal to:
[tex]\int\limits^5_0 {(2/5)x + 4 - (6/5)x} \, dx = \int\limits^5_0 {-(4/5)*x + 4} \, dx[/tex]
= (1/2)(-4/5)*(5)^2 + 4*5 - 0 = 10
The area is 10 squares
A 50 gram sample of a substance that's
used to treat thyroid disorders has a k
value of 0.1137.
The question is incomplete. Here is the complete question.
A 50 gram sample of a substance that's used to treat thyroid disorders has a k-value of 0.1137. Find the substance's half-life, in days. Round your answer to the nearest tenth.
Answer: [tex]t_{1/2}[/tex] = 6.1 days
Step-by-step explanation: Half-life is the amount of time necessary for a substance to reduce to half of its initial value.
To determine half-life through mass of a substance:
[tex]N = N_{0}.e^{-kt_{1/2}}[/tex]
Initially, there are 50 grams. After 1 half-life, there are 25 grams:
[tex]25 = 50.e^{-0.1137.t_{1/2}}[/tex]
[tex]\frac{25}{50} = e^{-0.1137.t_{1/2}}[/tex]
[tex]\frac{1}{2} = e^{-0.1137.t_{1/2}}[/tex]
[tex]ln (\frac{1}{2} ) = ln (e^{-0.1137.t_{1/2}})[/tex]
ln(1) - ln(2) = -0.1137.[tex]t_{1/2}[/tex]
[tex]t_{1/2} = \frac{- ln(2)}{- 0.1137}[/tex]
[tex]t_{1/2} =[/tex] 6.1
The half-life of the sample substance is 6.1 days.
What is the domain of the relation graphed below?
Answer:
domain: (-4,4)
Step-by-step explanation:
i'm not sure if it has brackets because it doesn't have point that are on x-intervals -4 and 4
Please answer this correctly
Answer:
1/64
Step-by-step explanation:
The probability of landing on a 7 is 1/8.
The probability of landing on a 2 is 1/8.
[tex]1/8 \times 1/8[/tex]
[tex]= 1/64[/tex]
1/64
The probability of landing on a 7 is 1/8.
The probability of landing on a 2 is 1/8.
1/8 \times 1/81/8×1/8
= 1/64=1/64
Assume that the probability of a driver getting into an accident is 4.2%, the
average cost of an accident is $13,547.92, and the overhead cost for an
insurance company per insured driver is $130. What should this driver's
insurance premium be?
A. $699.01
B. $56.90
C. $569.01
O D. $186.90
Answer:
A. $699.01
Step-by-step explanation:
130 = x − (0.042) (13547.92)
x = 699.01
10∑i i =6 10 is on top
Answer:
40
Step-by-step explanation:
We are using sigma notation to solve for a sum of arithmetic sequences:
The 10 stands for stop at i = 10 (inclusive)
The i = 6 stands for start at i = 6
The i stands for expression of each term in the sum
Work out percentage change to 2 decimal places when a price of £97 is increased to £99.99
Answer:
2.99
Step-by-step explanation:
99.99 - 97 = 2.99
The percentage change to 2 decimal places when a price of 97 is increased to 99.99 is 3.08%
What is percentage change?
Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.
Percentage Change Formulapercentage change formula = [tex]\frac{final value - initial value }{Initial value}[/tex]× 100
According to the given question
We have
initial value = 97
final value = 99.99
therefore,
⇒percentage change = [tex]\frac{99.99-97}{97}[/tex]× 100
⇒percentage change = [tex]\frac{2.99}{97}[/tex]×100
⇒percentage change = 0.0308×100=3.0824
⇒percentage change = 3.08%
Hence, the percentage change to 2 decimal places when a price of 97 increased to 99.99 is 3.08%.
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The sum of two intcgers is -6. If one of them is 2, then the other is
(a) 4
(b) 4
(c) 8
(d) -8
Answer:
D) -8
Step-by-step explanation:
If you add a positive and a negative, you end up subtracting. If your sum is lower than any of the numbers you are adding together, then there is a negative. In this case, your only negative number is -8, but if there were others, you could find this equation by doing negative six minus two (because the equation was originally addition, it would still be subtraction to check your work or find the answer in this case.)
Hopefully you find this useful :)
Answer: -8
Step-by-step explanation: lets take the unknown number as x,
so we have, 2 + x= -6
by using transposition method, x= -6-2( positive becomes
negative when transpositioning)
so, x= -8
A scooter runs 40 km using 1 litre of petrol tje distance covered by it using 15/4 litres of petrol is
Answer:
150 km
Step-by-step explanation:
1 liter ............ 40 km
15/4 liter .........x km
x = 15/4×40/1 = 600/4 = 150 km
Combine the like terms to create an equivalent expression: -12 - 6p - (-2)
Answer:
-6p -10
Step-by-step explanation:
-12 - 6p - (-2)
Subtracting a negative is like adding
-12 - 6p + (2)
Combine like terms
-6p -12+2
-6p -10
Answer:
-6p=10
Step-by-step explanation:
-12 - 6p - (-2) to combine like expression
-12-6p+2
-6p-10 to create equivalent expression an equal sign is used
-6p=10
Find the measure of the indicated angle to the nearest degree. Thanks.
Answer:
34
Step-by-step explanation:
uts obtuse angle
Answer:
16°
Step-by-step explanation:
Let x° be the missing angle:
cos x° = 53/55
cos x° = 0.963
using a calculator:
cos^(-1) (0.963) = 15.63 ≈ 16
Which one is cheaper and why
A bag of 4 litre milk for $3.99, or a carton of 1 litre milk for $1.99
Hey there! :)
Answer:
The bag is cheaper because one litre is roughly $1.00, compared to the carton which is $1.99 for one litre.
Step-by-step explanation:
Given:
Bag of 4 litre milk = $3.99
Carton of 1 litre milk = $1.99
Find the price per litre for a bag of milk:
[tex]\frac{3.99}{4} = \frac{x}{1}[/tex]
Cross multiply:
3.99 = 4x
Divide both sides by 4:
3.99/4 = x.
x = 0.9975 ≈ $1.00
Bag of 1 litre milk ≈ $1.00
Carton of 1 litre milk = $1.99
$1.00 < $1.99
Therefore, the bag is cheaper.
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. (Give answers to 2 decimal places) Store's Card Major Credit Card
Sample size 64 49Sample mean $140 $125Population variance $100 $641. A point estimate for the difference between the mean purchases of the users of the two credit cards is:________.2. At 95% confidence, the margin of error is:____________.3. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is___ to ___.
4. The test statistic for an alpha of .05 is:____________.
Answer:
Step-by-step explanation:
1) Point estimate is the difference between the sample means. Therefore,
A point estimate for the difference between the mean purchases of the users of the two credit cards is = 140 - 125 = $15
2) Margin of error = z√(σ²/n1 + σ2²/n2)
Where
z is the z score from the 95% confidence level. From the normal distribution table, z = 1.96
s1 and s2 are standard deviation for both customers respectively.
Standard deviation = √variance
σ1 = √100 = 10
σ2 = √641 = 25.32
Margin of error = 1.96√(10²/64 + 25.32²/49 = 7.5
At 95% confidence, the margin of error is 7.5
3) The confidence interval for the difference of two population means is expressed as point estimate ± margin of error
Confidence interval = 15 ± 7.5
The upper boundary for the confidence interval is
15 - 7.5 = 7.5
The lower boundary for the confidence interval is
15 + 7.5 = 22.5
A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is $7.5 to $22.5
4) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)
z = (x1 - x2)/(√σ1²/n2 + σ2²/n2)
z = (140 - 125)/√10²/64 + 25.32²/49
z = 1.02
The test statistic for an alpha of .05 is 1.02
what is the value of x in the equation 1/2x - 2/3 y = 30, when y = 15
Answer:
Step-by-step explanation:
1/2x - 2/3 × 15 = 30
1/2x - 10 = 30
1/2x = 30 + 10
1/2x = 40
x = 40 × 2
x = 80
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Which property of equality was used to solve this equation?
Answer:
Division property of equality
Step-by-step explanation:
They are dividing both sides.
what is the y-coordinate of point 7? Write a decimal coordinates.
Answer:
The y-coordinate is -4.5
Step-by-step explanation:
Point has x-coordinate -3 and y-coordinate -4.5.
Answer:
the y-coordinate is -4.5
Step-by-step explanation:
the x-coordinate is -3
the y-coordinate is in between -4 and -5. from here one can assume it is half way unless there is information that has not been stated.
In between -4 and -5 is -4.5 so the y-coordinate is -4.5
the coordinate of point 7 is ( -3, -4.5)
The total amount of deductions from an employee’s gross pay is $83.20. If the gross pay is $378.18, what percent of their gross pay is being withheld? a. 21% b. 22% c. 23% d. 24%
Answer: B. 22%
Step-by-step explanation:
Answer:
Yeah its 22%
Step-by-step explanation:
look at the right triangle ABC
Answer: A) Justification 1
Step-by-step explanation:
The student did not match the angles correctly.
∠ABC = 90° and ∠BCD = 60° so they cannot state that the angles are congruent. The other statement on that line is wrong also, but is irrelevant since there is already an error in that line.
Which of the following is a key property of the absolute value parent function?
A. It has a slope of 1 on the left half.
B. It is U-shaped
C. It is in quadrants I and ll
D. Its vertex is not at the origin
Answer:
the absolute-value parent function has a slope of 1 on the right half.
I hope this will work fine for you.
Comment if you need more explanation
ThX
Step-by-step explanation:
The tables show the number of chin-ups done by students in two different gym classes.
Answer:
On average, students in the 4th period Did more chin-ups than students in the 2nd period.