Answer:
Step-by-step explanation:
a = 8
b = 10
a^3 =8^3 = 512
b^3= 10^3 =1000
a^3 + b^3 = 1512
a^2 = 64
-ab = - 80
b^2 = 100
a + b=18
(a + b) (64 - 80+ 100)
18 * (84)
1512'
please hellppp please someone help me fast
Solve the system algebraically. 2x+ y - 10 = 0 x - y - 4 = 0 What is the value of y? 1/3 2/3 14/3
Answer:y = 2/3
Step-by-step explanation:
2x + y = 10
x - y = 4
-----------------add
3x = 14
x = 14/3
x - y = 4
14/3 - y = 4
-y = 4 - 14/3
-y = 12/3 - 14/3
-y = -2/3
y = 2/3 <==
Answer:
2x + y = 10
x - y = 4
-----------------add
3x = 14
x = 14/3
x - y = 4
14/3 - y = 4
-y = 4 - 14/3
-y = 12/3 - 14/3
-y = -2/3
y = 2/3 <==
Step-by-step explanation:
. A used car dealer says that the mean price of a two-year old sedan (in good condition) is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer's claim at a significance level (alpha) =0.05?
Answer: There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500
Step-by-step explanation:
given that;
n = 14
mean Ж = 19,850
standard deviation S = 1,084
degree of freedom df = n - 1 = ( 14 -1 ) = 13
H₀ : ц ≥ 20,500
H₁ : ц < 20,500
Now the test statistics
t = (Ж - ц) / ( s/√n)
t = ( 19850 - 20500) / ( 1084/√14)
t = -2.244
we know that our degree of freedom df = 13
from the table, the area under the t-distribution of the left of (t=-2.244) and for (df=13) is 0.0215
so P = 0.0215
significance ∝ = 0.05
we can confidently say that since our p value is less than the significance level, we reject the null hypothesis ( H₀ : ц ≥ 20,500 )
There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500
In the picture down below
Answer:
b
Step-by-step explanation:
The answer is b because we are looking for opposites
The opposite of +x is -x
While the opposite of -3 is +3
with this, we can switch them around.
this gives us the inverse of 3-x
please help! I don't understand how to do this :(
Simplify.
Remove all perfect squares from inside the square root. Assume y is positive.
√200y^4=
Answer:
[tex]10\sqrt{2[/tex]y²
Step-by-step explanation:
So I am not sure if the root is only on 200, but if it is not, please comment, and I will add to it.
what is the area of the triangle in the diagram?
Answer:
area=17.5
Step-by-step explanation:
area=1/2(base*height)
area=1/2(3*7)
are=17.5
Please help mee What is the smallest positive integer whose proper divisors add up to more than the integer itself?
Answer:
12
Step-by-step explanation:
The proper divisors of 12 are
1 2 3 4 6
Add those together you get 16
Choose the best estimate for the division problem below
6.7 /0.6
A. 16
B. 15
C. 11
Answer:
11
Step-by-step explanation:
6.7 / .6
Multiply top and bottom by 10
67/6
66/6 = 11 so this is close to 11
I need help!
- 7(x + 2) = 21
Answer:
x = -5
Step-by-step explanation:
-7(x + 2) = 21
Divide each side by -7
-7/-7(x + 2) = 21/-7
x+2 = -3
Subtract 2 from each side
x+2-2 = -3-2
x = -5
Answer:
x = -5
Step-by-step explanation:
distribute: -7x-14 = 21
add 14 to both sides
divide by -7
x = -5
Fredo has a coupon for $1.00 off the price of a loaf of bread at the grocery store.After he arrived at the store,he found out the bread had already been marked down $2.00.what is the total discount on the price of the bread.
Answer:
$3 discount
Step-by-step explanation:
If Fredo originally had the markdown as $0 (meaning no change), then he arrived at the store, seeing the markdown was $2, the current markdown is $2.
Now that he has an extra $1 off, he gets 2+1 = $3 off the bread.
Hope this helped!
The following data points represent the number of children in each household on Maple Street. \qquad 0, 1, 2, 1, 20,1,2,1,20, comma, 1, comma, 2, comma, 1, comma, 2 Find the mean number of children.
Answer:
The mean number of the children is 1.2
Step-by-step explanation:
Given
Children: 0, 1, 2, 1, 2
Required
Determine the Mean number
The mean of a set is calculated as follows;
[tex]Mean = \frac{\sum x}{n}[/tex]
Where x is the given set and n is the number of sets
In this case, n = 5 children
Hence;
[tex]Mean = \frac{0 + 1 + 2 + 1 + 2}{5}[/tex]
[tex]Mean = \frac{6}{5}[/tex]
[tex]Mean = 1.2[/tex]
Hence, the mean number of the children is 1.2
PQRS is a parallelogram. Find the values of a and b. Solve for the value of c if c = a + b.
A. 5
B. 14
C. 0
D. 7
Answer:
a = 7
b = 7
c = 14 [Correct option is B. 14]
Step-by-step explanation:
Since the shape is a parallelogram, to solve this problem, use some of the properties of a parallelogram:
(i) Opposite sides are parallel and congruent. Being congruent means the sides are identical. In other words, they have the same length.
From the diagram, this means that sides PQ and SR are identical. i.e
=> PQ = SR
=> 6a + 10 = 8a - 4 [collect like terms and solve]
=> 14 = 2a
=> a = 7
(ii) Opposite angles are congruent. Angles PQR and PSR are identical. i.e
<PQR = <PSR = (9b + 2)°
Also,
<SPQ = <SRQ = (18b - 11)°
(iii) Consecutive angles are supplementary. The sum of any two angles that are not opposite to each other is 180°. i.e.
<SPQ + <PQR = 180°
<PQR + <QRS = 180°
<QRS + <RSP = 180°
.
.
.
Also,
<PSR + <SPQ = 180°
(9b + 2)° + (18b - 11)° = 180° [expand bracket and solve for b]
9b + 2 + 18b - 11 = 180
27b - 9 = 180
27b = 189
b = 7
Now, since a = 7 and b = 7;
c = a + b = 7 + 7 = 14
Therefore;
a = 7
b = 7
c = 14
Tins of milk each of volume 77cm^3 and weight 170g
were packed into an empty carton of volume 1540cm^3
and weight 5ooo g.
How many tins of milk can be packed to fill the carton ?
What is the weight of the carton when packed with the tins of milk?
Answer:
1. 20 tins of milk
2. Weight of the Carton = 8,4kg ot 8400g
Step-by-step explanation:
Given
Volume of a Tin = 77cm³
Weight of a tin = 5000g
Volume of Empty Carton = 1540cm³
Weight of Empty Carton = 5000g
Calculating the number of tins of milk
To do this, we have to make use of the given volumes;
And this is done as follows;
[tex]Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}[/tex]
Substitute 77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton
[tex]Number = \frac{1540cm^3}{77cm^3}[/tex]
[tex]Number = 20[/tex]
Hence, 20 tins of milk will filled the empty carton
Calculating the weight of the Carton after filled with tins of milk
This is calculated as thus;
Total Weight = Weight of Empty Carton + Weight of Tins of Milk
Substitute 5000g for Weight of Empty Carton
Total Weight = 5000g + Weight of Tins of Milk
_________________________________________
Calculating Weight of Tins of Milk
Since 20 tins of milk will fill the empty carton, the
Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk
Weight of Tins of Milk = 20 * 170g
Weight of Tins of Milk = 3400g
_________________________________________
Substitute 3400g for Weight of Tins of Milk
[tex]Total\ Weight = 5000g + 3400g[/tex]
[tex]Total\ Weight = 8400g[/tex]
In Kilograms:
[tex]Total\ Weight = 8.4kg[/tex]
Simplify (8j3 − 10j2 − 7) − (6j3 − 10j2 − j + 12).
Answer:
Step-by-step explanation:
8j^3-10j^2-7-6j^3+10j^2+j-12
2j^3+j-12
What does x equal in the equation 4x + (−3) = 5x + 3?
Answer:
x = -6
Step-by-step explanation:
First write the equation.
4x + -3 = 5x + 3
The isolate x in the equation. Add -4x to both sides.
4x + -3 + -4x = 5x + 3 + -4x
-3 = x + 3
Then add -3 to both sides.
-3 + -3 = x + 3 + -3
-6 = x
Now you have the value of x = -6.
Cheers.
Answer:
x = -6Step-by-step explanation:
4x + (−3) = 5x + 3+3 +3
4x = 5x + 6-5x -5x
-x = 6÷(-1) ÷(-1)
x = - 6Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answer:
Below
Step-by-step explanation:
The canister has a cylindric form
The volume of a cylinder is given by the following formula :
V= r^2 * Pi *h
H is the heigth and r os the radius(half of the diameter)
Let Pi = 3.14
●●●●●●●●●●●●●●●●●●●●●●●●
V= 3.14*4.5^2 * 12
V= 763.02
V = 763 cm^3(after rounding to the nearest unit)
●●●●●●●●●●●●●●●●●●●●●●●●
The surface area of a cylinder is given by the followong formula:
Sa = 3.14*r^2*2 + Pi*d*h
r is the radius, d the diameter and h the heigth
Let Pi= 3.14
Sa= 3.14*4.5^2*2 + 3.14*9*12
Sa= 466.29 cm^2
Sa= 466 cm^2 ( after rounding to the nearest unit
●●●●●●●●●●●●●●●●●●●●●●●●
The dimensions of the second canister are the double of the first one
V= r^2*Pi*h
V= 9^2 *3.14*24
V= 6104.16 cm^3
V= 6104 cm^3 (after rounding to the neatest unit)
Sa= 2*3.14*r^2+ 3.14*d*h
Sa= 2*3.14*9^2 + 3.14*24*18
Sa= 1865.16 cm^2
Sa= 1865 cm^2 (after roundong to the nearest unit)
●●●●●●●●●●●●●●●●●●●●●●●●
The volume and the surface area of the second canister are bigger than the first one
Divide the second volume by the first one :
V2/V1= 6104/763 = 8
We deduce that the voulme of the second canister is greater 8 times than the first one
Do the same for the surface area
Sa2/Sa1 = 1865/466 = 4.002 = 4 (after rounding to the nearest unit)
The second surface area is greater 4 times than the first one
Answer:
Yeah, what they said above.
Step-by-step explanation:
HELP JOHN CHEN I need help
whats the principle square root of 100 A.10 B.50 C.200 D.10,000
Logan Chivery owns her own car. Her june monthly interest was $300. The rate is 8 1/2 percent. Logans principal balance at the beginning of June is $42,335.14.
Logan Chivery owns her own car. Her June monthly interest was $300. The rate is 8.5 percent. Logan's principal balance at the beginning of June is: (Use 360 days-do not round the denominator.)
A. $42,353.14
B. $42,335.14
C. $2,335.14
Answer: A. $42,353.14
Step-by-step explanation:
When taking a loan, we have to pay interest. The Simple Interest Formula is:
Simple Interest (I) = Principal (P) × Interest Rate (r)
Principal (P) is the borrowed amount.
Interest Rate (r) is the percent of the principal to be paid.
Time (t) is the length of time that money is borrowed.
If Logan Chivery has the monthly interest of $300 at a rate of 8.5% per year, first, we have to convert the year rate to the month of June rate.
30 days = 8.5÷360÷30 = 0.7083333333 interest rate
Then, find the Principal by using the formula
Simple Interest (I) = Principal (P) × Interest Rate (r)
4,2352.94×0.7083333333÷100=299.99
super easy problem its just graphing!! will mark brainliest <33
Answer:
[tex]y\ =\ \left|\frac{1}{2}x-2.5\right|+3[/tex]
Step-by-step explanation:
Look at the image below ↓
Answer:
Check below the graph.
Step-by-step explanation:
Hi, for this function, check the graph below:
1) Note that in this function the value outside the brackets points how high the graph will be traced.
2) The value within the brackets, points since it's a negative expression how far to the right the graph will be traced.
WILL GIVE BRAINLEIST!!!!!
Find the surface area of the right triangular prism shown below.
Answer:
144 units²
Step-by-step explanation:
Surface area of a traingular prism is given as:
Area = 2(B.A) + P*L
Where,
B.A = base area of the triangular prism = ½*b*h
b = base of the triangular base = 4 units
h = height of the triangular base = 3 units
Base Area (B.A) = ½*4*3 = 2*3 = 6 units²
P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units
L = length or height of prism = 11 units
Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L
[tex] Area = 2(6) + 12*11 [/tex]
[tex] = 12 + 132 [/tex]
[tex] Surface Area = 144 [/tex]
Surface area of the triangular prism = 144 units²
What are the zeros of the function y = 2x2 + 5x+2 ?
pls helppp!
Answer:
answer is a
Step-by-step explanation:
zeros are x intercepts
Answer:
A
Step-by-step explanation:
(2x+1)(x+2)
so
2x=-1
x=-1/2
x=-2
A
5/16 = 15/18 is proportion
Answer:
False
Step-by-step explanation:
In a proportion, the two fractions are equal. Here the denominators are different for the same numerator, so the fractions are not equal. The given expression is not a proportion.
The Pentagon building in Washington, DC is the military headquarters of the United States. Why is this building called the Pentagon? Among the redwoods in California, there’s a rustic inn and restaurant called The Hexagon House. From the name of the inn, how many walls can you assume the main building of the inn has? Jill bought a basket to fill with potpourri. The basket has eight sides. What shape is it? Write the correct name for each of the following polygons. a. A Shape b. A Shape c. A Shape d. A Shape Find the perimeter of each of the regular polygons described below. a. A square with sides measuring 6 centimeters b. An equilateral triangle with sides measuring 7 inches c. A regular heptagon with sides measuring 4 feet d. A regular nonagon with sides measuring 9 inches. Find the perimeter of each of the following polygons. Polygons Shelly is hanging strings of holiday lights around the front windows of her house. Each window is a square with sides measuring 5 feet in length. She has a total of 80 feet of light strings. How many windows will she be able to decorate? Use equations to find the length of the missing sides in each of the following polygons. a. A Shape b. A Shape c. A Shape d. A Shape
Answer:
1. It has 5 sides.
2. It has 6 walls.
3. Octagon
4. a. Pentagon (The figure has 5 sides.) b. Triangle (The figure has 3 sides.) c. Hexagon (The figure has 6 sides.) d. Hexagon (The figure has 6 sides.)
5. a. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm, or 4 × 6 cm = 24 cm, b. 7 in. + 7 in. + 7 in. = 21 in., or 3 × 7, in. = 21 in., c. 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. = 28 ft., or 7 × 4 ft. = 28 ft., d. 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. = 81 in., or 9 × 9 in. = 81 in.
6. a. 4 ft. + 3 ft. + 3 ft. + 2 ft. + 4 ft. + 5 ft. = 21 ft. b. 8 in. + 8 in. + 8 in. + 8 in. + 3 in. + 3 in. + 3 in. + 3in. = 44 in. c. 3 cm + 3 cm + 3 cm + 2 cm + 2 cm = 13 cm
7. Shelly has enough lights to decorate four windows.
8. a. 8 ft, b. 4 m, c. 24 ft, d. 7 cm
Step-by-step explanation:
PennFoster
Answer:
It has 5 sides.
It has 6 walls.
Octagon
a. Pentagon (The figure has 5 sides.)
b. Triangle (The figure has 3 sides.)
c. Hexagon (The figure has 6 sides.)
d. Hexagon (The figure has 6 sides.)
a. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm, or 4 × 6 cm = 24 cm
b. 7 in. + 7 in. + 7 in. = 21 in., or 3 × 7 in. = 21 in.
c. 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. = 28 ft., or 7 × 4 ft. = 28 ft.
d. 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. = 81 in., or 9 × 9 in. = 81 in.
a. 4 ft. + 3 ft. + 3 ft. + 2 ft. + 4 ft. + 5 ft. = 21 ft.
b. 8 in. + 8 in. + 8 in. + 8 in. + 3 in. + 3 in. + 3 in. + 3in. = 44 in.
c. 3 cm + 3 cm + 3 cm + 2 cm + 2 cm = 13 cm
Let w stand for the number of windows Shelly can decorate. Each window is a square with sides measuring 5 feet. The perimeter of one window is 4 × 5 feet. Divide the total length of the light strings by the perimeter of one window.
80 ft. ÷ (4 × 5ft.) = w
80ft. ÷ 20ft. = w
4 = w
Answer: Shelly has enough lights to decorate four windows.
Step-by-step explanation:
PENN
What is the volume of the cone? What is the volume of the cylinder? What is the volume of the sphere? At the craft store discussed above, the clay cone is $12, the clay cylinder is $30, and the clay sphere is $28. Which is the best buy? Explain. Hint: Which shapes gives you more clay for less money?
Answer:
clay sphere gives more clay for less money
Step-by-step explanation:
Volume of cone=1/3πr^2h
=1/3*3.14*(9^2)*12
=1/3*3.14*81*12
=3,052.08/3
=1017.36 inches^3
Volume of a cyclinder=πr^2h
=3.14*(9^2)*12
=3.14*81*12
=3,052.08 inches^3
Volume of a sphere=4/3πr^3
=4/3*3.14*(9^3)
=4/3*3.14*(9^3)
=4/3*3.14*729
=9,156.24 / 3
=3,052.08 inches^3
Clay cone=$12
Clay cyclinder=$30
Clay sphere=$28
Which is the best to buy
Comparing volume
Volume of sphere=3,052.08 inches^3
Volume of cyclinder=3,052.08 inches^3
Volume of cone=1017.36 inches^3
Sphere and cyclinder both have the same volume which is 3 times more than volume of a cone
Clay sphere cost $28 which is cheaper than clay cyclinder at the same volume.
Therefore, clay sphere gives more clay for less money
(h) 2/5 : 3/10
(i) 1/2 : 1/4: 1/6
(j) 2⅕ : 1¼ : 1⅕
express the following ratios in the simplest form.
Answer:
4/3
12
44/30
Step-by-step explanation:
2/5:3/10
=2/5*10/3
=20/15
=4/3
1/2:1/4:1/6
=1/2*4/1*6/1
=4/2*6/1
=24/2
=12
2⅕:1¼:1⅕
11/5:5/4:6/5
=11/5*4/5*5/6
=44/25*5/6
=220/150
=44/30
Hope this helps ;) ❤❤❤
A company can make 12 printing presses for $78,600. It can make 19 printing presses for $82,380. Find the linear equation that models the cost to produce x printing presses. Use slope-intercept form
Answer:
[tex]C(x) = 540x + 72120[/tex]
Step-by-step explanation:
Given
Cost = $78,600 when Printing Press = 12
Cost = $82,380 when Printing Press = 19
Required
Determine the linear equation
From the given parameters; Cost is a function of Printing Press
Represent Cost by C and Printing press by x;
This implies that C = f(x)
The given parameters can then be modeled as; [tex](x, C)[/tex]
[tex](x_1, C_1) = (12,78600)[/tex]
[tex](x_2, C_2) = (19,82380)[/tex]
The first step is to calculate the slope, m;
[tex]m = \frac{C_1 - C_2}{x_1 - x_2}[/tex]
[tex]m = \frac{78600 - 82380}{12 - 19}[/tex]
[tex]m = \frac{-3780}{-7}[/tex]
[tex]m = 540[/tex]
The linear equation can then be calculated using slope formula
[tex]m = \frac{C- C_2}{x - x_2}[/tex]
Substitute 540 for m and [tex](x_2, C_2) = (19,82380)[/tex]
[tex]540 = \frac{C- 82380}{x - 19}[/tex]
Multiply both sides by x - 19
[tex]540 * (x-19)= \frac{C- 82380}{x - 19} * (x-19)[/tex]
[tex]540 * (x-19)= C- 82380[/tex]
Open bracket
[tex]540x - 10260 = C - 82380[/tex]
Add 82380 to both sides
[tex]540x - 10260 + 82380= C - 82380 + 82380[/tex]
[tex]540x - 10260 + 82380= C[/tex]
[tex]540x + 72120= C[/tex]
[tex]C = 540x + 72120[/tex]
Hence;
[tex]C(x) = 540x + 72120[/tex]
Jason is playing a trivia game with his friends. At the end of each round, his score updates to the square of 1 less than the previous round’s score. If he has 8 points in the first round, which of the following recursive formulas can be used to determine his score at the end of future rounds? Assume that the number of rounds is unlimited, and n is the number of rounds.
Answer:
8+n^2
Step-by-step explanation:
Answer:
f(n+1)=(f[n]-1)^2, where f(1)=8
Step-by-step explanation:
"it appears your explanation includes a link" so you don't get an explanation
Let $f(x)=x+5$ and let $g(x)=x^2+1$. Let $p(x)=g(x)+f(x)$ and let $q(x)=g(x)-f(x)$. Find $p(x)\cdot q(x)$.
Answer:
The data that we have is:
f(x) = x + 5
g(x) = x^2 + 1
p(x) = g(x) + f(x) = (x^2 + 1) + (x + 5) = x^2 + x + 6.
q(x) = g(x) - f(x) = (x^2 + 1) - (x + 5) = x^2 - x - 4
We want to find p(x)*q(x)
well, we can replace:
p(x)*g(x) = (g(x) + f(x))*(g(x) - f(x))
Now, you can recall the relationship:
a^2 - b^2 = (a + b)*(a - b)
then we have that:
(g(x) + f(x))*(g(x) - f(x)) = g(x)^2 - f(x)^2
now we can replace g(x) and f(x) by the expressions that we know:
g(x)^2 - f(x)^2 = (x^2 + 1)^2 - (x + 5)^2
now we can simplify this:
(x^2 + 1)^2 - (x + 5)^2 = (x^4 + 2*1*x + 1^2) - (x^2 + 2*5*x +5^2)
= x^4 + 2*x + 1 - x^2 - 10x - 25
= x^4 - x^2 - 8*x - 24
p(x)*q(x) = x^4 - x^2 - 8*x - 24
Answer:
x^4+x^2-10x-24
Step-by-step explanation:
For the inequality y+4x≤x2+2, where is the graph shaded and is the curve solid or dotted?
Answer:
The graph shaded outside the parabola and the curve is solid.
Step-by-step explanation:
The given inequality is
[tex]y+4x\leq x^2+2[/tex]
It can be rewritten as
[tex]y\leq x^2-4x+2[/tex]
The sign of inequality is [tex]\leq[/tex], so the curve is a solid line.
The related equation of line is
[tex]y=x^2-4x+2[/tex]
Table of values is
x 0 2 4
y 2 -2 2
Plot these points and draw a U-shaped curve.
Check the equality for (0,0).
[tex]0\leq (0)^2-4(0)+2[/tex]
[tex]0\leq 2[/tex]
This statement is true. So, (0,0) lies in the shaded portion.
So, shade the graph outside the parabola.