300(1.08)^5
440.798423
What is the area of the trapezoid shown below?
Answer:
[tex]\Large \boxed{\mathrm{78 \ units^2 }}[/tex]
Step-by-step explanation:
The area of the trapezoid can be found by adding the area of the triangle and the area of the rectangle.
Area of rectangle = base × height = 2 × 12 = 24 units²
Area of triangle = base × height × 1/2
The base is missing for the triangle. Apply Pythagorean theorem to solve for the base.
12² + b² = 15²
b = 9
9 × 12 × 1/2 = 54 units²
Adding the areas.
54 units² + 24 units² = 78 units²
Answer:
its 78 units on khan academy :)))
Step-by-step explanation:
help will mark brainlist if it correct If each edge of a cube is increased by 2 inches, the
A. volume is increased by 8 cubic inches
B. area of each face is increased by 4 square
C. diagonals of each face is increased by 2 inches
D. sum of these edges is increased by 24 inches
Answer:
D. sum of these edges is increased by 24 inches -- True
Step-by-step explanation:
Given a cube and its edge is increased by 2 inches.
To study the effect of this increase in the Volume, area of each face, diagonal and sum of edges.
Solution:
Let the side of original cube = a inches.
Formula for volume of cube:
[tex]V =side^3 = a^3[/tex]
If the side is increased by 2 inches, the side becomes (a+2) inches.
So, new volume, [tex]V' = (a+2)^3[/tex]
Using the formula:
[tex](x+y)^3 =x^3+y^3+3xy(x+y)[/tex]
[tex]V' = (a+2)^3 = a^3+8+3\times 2 \times a(a+2)=a^3+8+6a(a+2)[/tex]
So, [tex]V' = V + 8+6a(a+2)[/tex]
Volume increased by 8+6a(a+2) [which is not equal to 8]
So, statement is false:
A. volume is increased by 8 cubic inches -- False
Each face in a cube is a square.
Area of each face, A = [tex]side^2 = a^2[/tex]
New area, A' = [tex](a+2)^2[/tex]
Using the formula: [tex](x+y)^2 =x^2+y^2+2xy[/tex]
[tex]A' = a^2+4+4a[/tex]
Area increased by 4+4a [which is not equal to 4 sq inches]
B. area of each face is increased by 4 square inches -- False
Diagonal of each face = [tex]a\sqrt2[/tex]
Increase of 2 in the edge:
New diagonal = [tex](a+2)\sqrt2 = a\sqrt2+2\sqrt2[/tex]
So, increase of [tex]2\sqrt2[/tex] not 2.
C. diagonals of each face is increased by 2 inches -- False
There are 12 number of edges in a square.
So sum of all 12 edges = 12a
When edge is increased by 2, sum of all edges = 12(a+2) = 12a + 24
An increase of 24.
D. sum of these edges is increased by 24 inches -- True
Melissa, of Melissa's Lawn and Landscaping Service, needs to replace her mowers.
She has ordered four new gas mowers, at $499 each, and a negotiated Trade
Discount Rate of 9%, with terms of 2/10 EOM, and FOB Shipping Point. The
seller has agreed to prepay the shipping charge of $80, which is not included in the
invoice amount. The invoice from the manufacturer is dated July 26.
Determine:
A)
By what date does Melissa have to pay in order to be able to take the cash
discount?
B)
What is the payment amount assuming that Melissa pays before the end of
the discount period?
Answer:
A) 10th of August
B) $1780.03
Step-by-step explanation:
A) From the payment terms of 2/10 EOM, Melissa is to receive a 2% discount if she pays within 10 days from the end of the month
From the date on the invoice, July 26, the date at which Melissa has to pay to take the cash discount is before the 10th of August
B) The payment amount will be 2% off the original payment amount
The total cost of the four new gas mowers less the trade discount = 499 × 4 × (100 - 9)/100 =$1816.36
The 2% discount will then be $1816.36 × (100 - 2)/100 = $1780.03
The payment amount assuming Melissa pays before the end of the discount period = $1780.03.
What two numbers multiply to negative 12 and add up to negative 13
Answer:
−13.8654599313 and 0.8654599313
Step-by-step explanation:
The two numbers of interest will be the solutions to ...
xy = -12
x +y = -13
Substituting for y, this becomes the quadratic ...
x(-13 -x) = -12
x^2 +13x = 12 . . . . . multiply by -1
x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square
(x +6.5)^2 = 54.25
x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5
x ≈ -13.865499313 or 0.8654599313
The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.
The graph of g(x) is a translation of the function f(x)=x^2. The vertex of g(x) dislocated five units above and seven units to the right of the vertex of f(x). which equation represents g(x)
[tex]f(x)[/tex] passes through origin, i.e. $(0,0)$
if you move 5 units up, it should pass through $(0,5)$
so you'll add 5 to $y$ i.e. $y+5=x^2$ this satisfies $(0,5)$
and to move right, it should pass through $(7,0)$ so you'll subtract $7$ from $x$ i.e. $y=(x-7)^2$
now combine both translations
$g(x)=(x-7)^2-5=x^2-14x+45$
Please help with this question!!!!!
===================================
Explanation:
Start with the parent function [tex]y = |x|[/tex]
Replacing x with x-1 shifts the graph 1 unit to the right
Tack a -1 at the end to get [tex]y = |x-1|-1[/tex] which will shift everything down 1 unit.
The vertex started at (0,0) and moved to (1,-1)
Which of the following statements is true about odd
and/or even numbers?
F. The sum of any 2 even numbers is odd.
G. The sum of any 2 odd numbers is ood.
H. The quotient of any 2 even numbers is odd.
J. The quotient of any 2 even numbers is even.
K. The product of any 2 odd numbers is odd.
Answer:
k) the product of ant 2 odd numbers is odd
I don't know.
Let's check um out.
For each choice, I'll try to find an example to show that it's false.
F. The sum of any 2 even numbers is odd.
2+2=4. 4 is even. This one is false.
G. The sum of any 2 odd numbers is ood.
3+3=6. 6 is even. This one is false.
H. The quotient of any 2 even numbers is odd.
8÷4=2. 2 is even. 10÷4=2.5. 2.5 is neither odd nor even. This one is false.
J. The quotient of any 2 even numbers is even.
10÷2=5. 5 is odd. This one is false.
K. The product of any 2 odd numbers is odd.
I can't find an example where this is false.
So I'm gonna say that this is the true one.
Can someone help?...look at the pics
Answer:
[tex]\boxed{y=2x-2}[/tex]
Step-by-step explanation:
Pick values from the table.
When x = 1, y = 0.
The third option seems right.
[tex]y=2(1)-2[/tex]
[tex]y=2-2[/tex]
[tex]y=0[/tex]
True.
Evaluate 2x+3x+2 for x= -2
Answer:
-8
Step-by-step explanation:
2(-2) +3(-2) +2
-4 -6 +2
-10 +2
-8
NEED HELP ASAP solve for x : 3/5 = x-1/8
a.5 b.29/5 c.23/5 d.19/5
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{ \frac{29}{5} }}}}}[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \sf{ \frac{3}{5} = \frac{x - 1}{8} }[/tex]
Apply cross product property
⇒[tex] \sf{ 5(x - 1) = 3 \times 8}[/tex]
Distribute 5 through the parentheses
⇒[tex] \sf{5x - 5 = 3 \times 8}[/tex]
Multiply the numbers
⇒[tex] \sf{5x - 5 = 24}[/tex]
Move 5 to right hand side and change it's sign
⇒[tex] \sf{5x = 24 + 5}[/tex]
Add the numbers
⇒[tex] \sf{5x = 29}[/tex]
Divide both sides of the equation by 5
⇒[tex] \sf{ \frac{5x}{5} = \frac{29}{5} }[/tex]
⇒[tex] \sf{x = \frac{29}{5} }[/tex]
Hope I helped!
Best regards!!
PLEASE HELP How can a company use a scatter plot to make future sale decisions
Answer:
From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.
Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).
Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).
Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
Answer:
The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2
Step-by-step explanation:
Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.
Therefore:
x + y = z (1)
Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:
Cost of buying = Price it was sold for
The cost of the mango = 5z and the price it was sold for = 3x + 6y
3x + 6y = 5z (2)
Substituting z = x + y in equation 1
3x + 6y = 5(x + y)
3x + 6y = 5x + 5y
6y - 5y = 5x - 3x
y = 2x
x / y = 1/ 2 = 1 : 2
The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2
Help please! How would I solve a 2 step equation like this? 4(x-2)=14
Answer: Hi!
Okay. So this equation we will solve using something called the distributive property. We use the distributive property to multiply the terms inside the parentheses (x and -2) by the term outside and in front of the parentheses (4). First, we would multiply 4 * x, which is 4x. Then, we would multiply 4 * -2, which is -8. Out equation now looks like this:
4x - 8 = 14
Our goal is to isolate the x, so now we'll use inverse operations to remove the -8 from the equation. The inverse operation for subtraction is addition, so we would add 8 to both sides:
4x - 8 = 14
+ 8 + 8
The eights cancel out, so we're left with this equation:
4x = 22
Last step! We're almost done. All we have to do now is divide 4 on both sides; in the term 4x, 4 is being multiplied by x, so the inverse operation would be division.
4x ÷ 4 = x
22 ÷ 4 = 5.5
Our equation now looks like this:
x = 5.5
So, 5.5 is equal to x! This would be your answer!
Hope this helps!
Can you help Jorge organize the results into a two-way frequency table?
Answer:
Top left: 6
Bottom left: 8
Top right: 7
Bottom right: 3
Step-by-step explanation:
To solve this problem, we need to look at the table to see what missing information we need to solve for. On the table, it asks us how many students:
Play a musical instrument and sportDoesn't play anythingPlays sportsPlays an instrumentOn the first intersection (top left), we are asked how many students played an instrument and sport. That is easy to solve because the information they provide us already gives us that number: 6.
On the second intersection (bottom left), things get a little more challenging. The information states that 14 students in total play sports, so that is not the number of people who only play sports. Since 14 people in total play sports and 6 people play both an instrument and sport, we subtract 6 from 14 to get our answer, 8.
On the third intersection (top right), it asks us how many people play an instrument but doesn't play a sport. Let's look at the remaining values first. There is: 6, 8, 3. When we add those together, we get 17, and when we subtract that from the total (24), we get our answer: 7.
On the last intersection (bottom right), the information already provides us with the answer to how many people don't play anything: 3.
8 m minus 6 less or equal than 10
Hi there! :)
Answer:
[tex]\huge\boxed{m\leq 2}[/tex]
Equation:
8m - 6 ≤ 10
Add 6 to both sides:
8m ≤ 16
Divide both sides by 8:
8m/8 ≤ 16/8
m ≤ 2
Answer:
8m - 6≤ 10
m≤2
Step-by-step explanation:
8m - 6≤ 10
Add 6 to each side
8m - 6+6≤ 10+6
8m ≤ 16
Divide each side by 8
8m/8 ≤16/8
m≤2
An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 5% and 95% confidence. To gauge the size of the problem, the agency first picks 50 cars and finds 12 with faulty emissions systems. How many should be sampled for a full investigation?
Answer:
197
Step-by-step explanation:
Sample proportion is; p^ = 12/50 = 0.24
Margin of error of 5% is given by the formula;
ME = (z_0.05) √[p^(1 - p^)/n]
Let's make n(number of sample) the subject.
n = ((z_0.05)/ME)²((p^)(1 - p^))
From tables, the z-score of 0.05 is 1.645
Thus;
n = ((1.645)/0.05)²(0.24(1 - 0.24))
n ≈ 197
solve 2(1/9)× = 2/81 for x
Answer: x=1/9
Step-by-step explanation:
[tex]2\left(\frac{1}{9}\right)x=\frac{2}{81}[/tex]
[tex]\frac{2}{9}x=\frac{2}{81}[/tex]
multiply both sides by 9
[tex]9\cdot \frac{2}{9}x=\frac{2\cdot \:9}{81}[/tex]
[tex]2x=\frac{2}{9}[/tex]
divide 2 on both sides
[tex]x=\frac{1}{9}[/tex]
State the null and alternative hypothesis in each case.
(a) A hypothesis test will be used to potentially provide evidence that the population mean is less than 5.
(b) A hypothesis test will be used to potentially provide evidence that the population mean is more than 10.
(c) A hypothesis test will be used to potentially provide evidence that the population mean is not equal to 7
Answer:
Which term is a term in this expression?
Step-by-step explanation:
Which term is a term in this expression?Which term is a term in this expression?Which term is a term in this expression?Which term is a term in this expression?Which in this expression?Which term is a term in this expression?
Will give brainliest. Find the length and measure of each arc. Show your work.
Problem 1
The circumference is the full perimeter around the circle. You can think of it as the combination of "circle" and "fence" to get "circumference", but there might be other tricks to remember the term.
Anyways, the formula to get the circumference of a circle is
C = 2*pi*r
In this case, r = 14 is our radius so,
C = 2*pi*r
C = 2*pi*14
C = 28pi .... exact circumference in terms of pi
We only want a portion of this circumference as shown by the piece of the circle darkened. The fractional portion we want is 135/360 of a circle. Divide the angle by 360 to get the fractional portion you want. If the angle was say 180 degrees, then 180/360 = 1/2 is the fractional portion.
So we take 135/360 and multiply it by the value of C found earlier
arc length = (fractional portion)*(circumference)
arc length = (135/360)*28pi
arc length = 10.5pi
That's the exact arc length in terms of pi. Use a calculator to find that
10.5pi = 32.9867228626929
Or you could use pi = 3.14 to say
10.5*pi = 10.5*3.14 = 32.97
Which is fairly close to what the calculator is saying
-----------------
Summary:Exact arc length = 28pi
Approximate arc length (using calculator) = 32.9867228626929
Approximate arc length (using 3.14 for pi) = 32.97
Units are in feet
When I write "using calculator", I mean using the calculator's stored version of pi, instead of pi = 3.14
======================================================
Problem 2
We could use the same idea as problem 1, or we could use the formula below. The formula is just a quick way of encapsulating what I discussed earlier.
L = arc length
x = central angle
L = (x/360)*2*pi*r
L = (150/360)*2pi*13
L = (65/6)pi .... exact arc length
L = 34.0339204138894 .... approx arc length (using calculator)
L = 34.0166666666667 .... approx arc length (using 3.14 for pi)
-----------------
Summary:Exact arc length = (65/6)pi
Approximate arc length (using calculator) = 34.0339204138894
Approximate arc length (using 3.14 for pi) = 34.0166666666667
Units are in meters
Express in standard form : a) 0.000000056 b) 56780000000 c) 1923.8 (will mark brainly
Answer:
Step-by-step explanation:
a) 5.6 x 10∧-8
b) 5.678 x 10∧10
c) 1.9238 x 10∧3
math be like 0-0????
Answer: A & C
Step-by-step explanation:
HL is Hypotenuse-Leg
A) the hypotenuse from ΔABC ≡ the hypotenuse from ΔFGH
a leg from ΔABC ≡ a leg from ΔFGH
Therefore HL Congruency Theorem can be used to prove ΔABC ≡ ΔFGH
B) a leg from ΔABC ≡ a leg from ΔFGH
the other leg from ΔABC ≡ the other leg from ΔFGH
Therefore LL (not HL) Congruency Theorem can be used.
C) the hypotenuse from ΔABC ≡ the hypotenuse from ΔFGH
at least one leg from ΔABC ≡ at least one leg from ΔFGH
Therefore HL Congruency Theorem can be used to prove ΔABC ≡ ΔFGH
D) an angle from ΔABC ≡ an angle from ΔFGH
the other angle from ΔABC ≡ the other angle from ΔFGH
AA cannot be used for congruence.
If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?
Answer:
is it 2
Step-by-step explanation:
Barbara Cusumano worked 60 hours last week. Of those hours, 40 hours were paid at the regular-time rate of $12.50 an hour, 18 hours at the time-and-a-half rate, and 2 hours at the double-time rate. What was Barbara's gross pay for the week?
Answer:
$887.50
Step-by-step explanation:
Her gross pay is the sum of the pay amounts for each of the hour amounts:
pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)
= (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)
pay = 887.50
Barbara's gross pay for the week was $887.50.
Given TS¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ are midsegments, PR=18.2, TS=6.5. Find QU . A. 9.1 B. 3.25 C. 13 D. 6.5
Answer:
The correct option is;
D. 6,5
Step-by-step explanation:
TS and TU are midsegments
Segment PR = 18.2
Segment TS = 6.5
Given that TS is the midsegment of PR and PQ, therefore, TS = 1/2×QR
Which gives;
Segment QR = 2×TS = 2 × 6.5 = 13
Segment QR = 13
Given that TU is a midsegment to PQ and QR, we have that QU = UR
Segment QR = QU + UR (segment addition postulate)
Therefore, QR = QU + QU (substitute property of equality)
Which gives;
QR = 2×QU
13 = 2×QU
Segment QU = 13/2 = 6.5
The length of segment QU is 6.5.
Evaluate the expression 18C4
Answer:
3,060
Step-by-step explanation:
Given:
18C4
nCr=n! / r!(n-r)!
=18! / 4!(18-4)!
18!=18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
=6,402,373,705,728,000
4!=4*3*2*1
=24
(18-4)!=14!
=14*13*12*11*10*9*8*7*6*5*4*3*2*1
=87,178,291,200
18! / 4!(18-4)!
=6,402,373,705,728,000 / 24*87,178,291,200
=6,402,373,705,728,000 / 2,092,278,988,800
=3,060
find the gcd of 12 18 and 24
Answer:
6
Step-by-step explanation:
the solution in photo :)
Answer:
6
Step-by-step explanation:
→ Prime factorise each number
12 = 2² × 3 ⇒ 2 × 2 × 3
18 = 2 × 3² ⇒ 2 × 3 × 3
24 = 2³ × 3 ⇒ 2 × 2 × 2 × 3
→ Find which number there are in each one
2 and 3
→ Multiply them together
2 × 3 = 6
What is the formula to find the area of the sector?
Answer:
There are 3 ways
Step-by-step explanation:
The formula for a sector's area is:
1. A = (sector angle / 360 ) * (pi *r2)
2. A = (sector angle / (2*pi)) * (pi * r2)
3. A = (fraction of the circle) * (pi * r2)
Help, Answer ASAP; will give brainliest
Answer:
PY = 14.5
Step-by-step explanation:
The diagonals of a rectangle are congruent and bisect each other, thus
XZ = WY , that is
4x - 1 = x + 7 + x + 7
4x - 1 = 2x + 14 ( subtract 2x from both sides )
2x - 1 = 14 ( add 1 to both sides )
2x = 15 ( divide both sides by 2 )
x = 7.5
Thus
PY = x + t = 7.5 + 7 = 14.5
Step-by-step explanation:
py is equal to wp because the figure is a rectangle.x+7+x+7= 4x-1
2x+14=4x-1
14= 2x-1
15= 2x (divide)
x = 7.5
wp= 7.5cm
not really sure
You double the radius of a circle. Predict what will happen tothe circle’s circumference and what will happen to its area. Test yourprediction for a few circles. Use a different radius for each circle. Thenpredict how doubling a circle’s diameter will affect its circumferenceand area. Test your prediction for a few circles with different diameters.
Answer:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
Step-by-step explanation:
Given that
Radius of a circle is doubled.
Diameter of circle is doubled.
To study:
The effect on circumference and area on doubling the radius and diameter.
Solution/explanation:
Let us discuss about the formula for circumference and area.
Formula for Circumference of a circle in form of radius:
[tex]C =2\pi r[/tex]
It is a linear equation in 'r'. So by doubling the radius will double the circumference.
Formula for Area of a circle in form of radius:
[tex]A =\pi r^2[/tex]
It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.
Testing using example:
Let the initial radius of a circle = 7 cm
Initial circumference = [tex]2 \times \frac{22}{7} \times 7 = 44 cm[/tex]
Initial area = [tex]\frac{22}{7} \times 7 \times 7 =154 cm^2[/tex]
After doubling:
Radius = 14 cm
circumference = [tex]2 \times \frac{22}{7} \times 14 = 88 cm[/tex] (Twice the initial circumference)
area = [tex]\frac{22}{7} \times 14 \times 14 =616 cm^2[/tex] (4 times the initial area)
------------------------------------
Formula for Circumference of a circle in form of Diameter:
[tex]C =\pi D[/tex]
It is a linear equation in 'D'. So by doubling the diameter will double the circumference.
Formula for Area of a circle in form of diameter:
[tex]A =\dfrac{1}{4}\pi D^2[/tex]
It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.
Testing using example:
Let the initial diameter of a circle = 28 cm
Initial circumference = [tex]\frac{22}{7} \times 28 = 88 cm[/tex]
Initial area = [tex]\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2[/tex]
After doubling:
Diameter = 56 cm
circumference = [tex]\frac{22}{7} \times 56= 176 cm[/tex] (Twice the initial circumference)
area = [tex]\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2[/tex] (4 times the initial area)
So, the answer is justified:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
f(x)=2-3x domain= {-1,0,1,2}
Answer:
range = {5, 2, -1, -4}
Step-by-step explanation:
Maybe you want the corresponding range.
f({-1, 0, 1, 2}) = 2 -3{-1, 0, 1, 2} = 2 +{3, 0, -3, -6} = {5, 2, -1, -4}
