Using the distributive property, it is found that the equivalent expression is:
18c - 30d + 36
What is the distributive property?It is a property that the outside term multiplies each of the inside terms.
In this problem, the expression is:
6(3c - 5d + 6).
Hence, we apply the property, with the outside term 6 multiplying each of the inside terms, hence the equivalent expression is given by:
6(3c - 5d + 6) = 18c - 30d + 36.
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The area of a circle is 4π ft². What is the circumference, in feet? Express your answer in terms of \piπ.
Answer:
4π ft.
Step-by-step explanation:
Area = π r^2 = 4π = π2^2
- so the radius is 2 ft,
and the circumfrence = 2 π r
= 2*π*2
= 4π ft.
The circumference of the circle is 4π feet.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
The formula for the area A of a circle with radius r is given by:
A = πr²
We are given that the area of the circle is 4π ft², so we can set up the following equation:
4π = πr²
Dividing both sides by π, we get:
r² = 4
Taking the square root of both sides, we get:
r = 2
The circumference C of a circle with radius r is given by:
C = 2πr
Substituting r = 2, we get:
C = 2π(2) = 4π
Therefore,
The circumference of the circle is 4π feet.
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Four years from now, hozumi will be 2 years younger than 4 times her present age. which equation could be used to determine hozumi’s age ( h ) now, and what is her age?
Answer:
2
Step-by-step explanation:
Four years from now: h+4
Hozumi will be 2 years younger than 4 times her present age: 4h-2
h+4=4h-2
6=3h
h=2
Write the following arithmetic series in summation notation.
7+9+11+ . . . +35
..
Answer:
[tex]S_{n}=315[/tex]
Step-by-step explanation:
[tex]a_{1}=7\\a_{2}=9\\a_{n}=35\\[/tex]
d=9-7=2
no of terms n,
[tex]n=\frac{a_{n-a_{1}} }{d} +1[/tex]
[tex]n=\frac{{35}-{7}}{2} +1[/tex]
[tex]n=15[/tex]
sum of series,
[tex]S_{n}=\frac{n}{2} (a_{1}+a_{n})\\\\S_{n}=\frac{15}{2} (7+35})\\\\S_{n}=315[/tex]
Complete the frequency table for the following set of data.
Step-by-step explanation:
+
Please can u look at the following
Answer:
a) x = -10
b) x = 7
Step-by-step explanation:
a)
2(x+3) = x - 4
==> distribute the 2
2x + 6 = x - 4
==> add 4 to both sides
2x + 10 = x
==> subtract 2x from both sides
10 = -x
==> divide both sides by -1
x = -10
b)
4(5x - 2) = 2(9x + 3)
==> distribute the 4 and 2
20x - 8 = 18x + 6
==> add 8 to both sides
20x = 18x + 14
==> subtract 18x from both sides
2x = 14
==> divide both sides by 2
x = 7
Christina is 11 years older than caden. the sum of their ages is 35. how old is christina? how old is caden?
Answer:
Caden is 11 and Christina is 24.
Step-by-step explanation: IF we know the sum of their ages is 35, then we can do the math. 35 - 11 = 24
So this means we know two ages 11 and 24.
The only thing left to do is to figure out who's age is who's. We know that Christina is older so she has to be 24 year old and Caden would be younger.
I hope this helps!
an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. the heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the legnth of the shorter base of each trapezoid is 1.5 centimeters. what is the total area of the face of the watch to the nearest tenth of a square centimemter
Answer:
Step-by-step explanation:
The total area of the face of the watch is 9.0 cm²
What is a hexagon?The polygon with six side is called a hexagon.
Given that, a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached.
height, h = apothem of the hexagon = 2 cm and
base, b = length of shorter base of trapezoid.
Area of the triangle
So, the area of this triangle is A = 1/2bh
= 1/2 × 1. 5 cm × 2 cm
= 1.5 cm × 1 cm
= 1.5 cm²
Area of the hexagon
Since there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A
= 6 × 1.5 cm²
= 9.0 cm²
So, total area of the face of the watch is 9.0 cm²
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The top of Mrs. Vonvilla’s coffee table has the dimensions shown. She wants to put a bumper around the edges of the table to protect her child in case he falls. What is the perimeter of the tabletop?
A coffee table has a length of 48 inches and a width of 28 inches.
Use the formula for the perimeter of a rectangle, P = 2 l + 2 w, where P is the perimeter, l is the length, and w is the width.
76 in.
152 in.
304 in.
1,344 in.
Answer:
152 inch
Step-by-step explanation:
The dimensions of tha coffee table are .
The perimeter of a rectangle is defined as , where is the length and is the width.
So, by given we have
If we use the formula for the perimeter of a rectangle and substitute each variable, then we would have
The perimeter of the coffee table is 152 inches.
To celebrate the first day of school, Nathan brought in a tray of caramel brownies and walnut brownies. He brought 100 brownies in all. 4 of the brownies were caramel. What percentage of the brownies were caramel?
Answer:
Step-by-step explanation:
Out of 100 brownies ,4 were caramel.
Ratio of Caramel Brownies to Brownies: 4/100
If you further simplify it , 4/100 is the same thing as 1/25 , which can also be expressed as
Answer: 4% of the brownies were caramel
When Brooklyn runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard deviation of 3 seconds. Using the empirical rule, what percentage of races will her finishing time be between 70 and 82 seconds?
Using the Empirical Rule, it is found that her finishing time will be between 70 and 82 seconds in 95% of her races.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, the mean is of 76 seconds and the standard deviation is of 3 seconds, then:
76 - 2 x 3 = 70.
76 + 2 x 3 = 82.
Which means that values between 70 and 82 seconds are within 2 standard deviations of the mean, hence the percentage is of 95%.
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the price of 5 boxes of crackers at the store can be represented by the equation $17.75 divide 5 = k what would be the cost of 7 boxes of crackers
Answer:
24.85
Step-by-step explanation:
17.75/5 = 3.55
3.55 x 7 = 24.85 :)
Have an awesome day!
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1. If PQ || SR and PQRS is an isosceles trapezoid,
find m<1.
A. 30°
B. 32°
C. 34°
D. 36°
Answer:
B. 32°
Step-by-step explanation:
Finding ∠S and ∠R
∠S = 58°∠S = ∠R (Isoceles trapezoid)⇒ ∠R = 58°Similarly, ∠P = ∠Q (same reason as above)
Applying the Angle Sum Property of Quadrilaterals,
∠P + ∠Q + ∠R + ∠S = 360°2∠P + 2∠S = 360°∠P + ∠S = 180°∠P = 180° - 58°∠P = 122° = ∠QFinding the missing angles of the triangle
Left angle : ∠x + 96° = 122°∠x = 26°Applying the Angle Sum Property of Triangles,
∠x + ∠Q + ∠1 = 180°26° + 122° + ∠1 = 180°∠1 = 180° - 148°∠1 = 32°Please help I will give brainliest.
Answer:
c = 9
Step-by-step explanation:
You're looking for a number so that when you use that number in place of x, you end up with 20.
f(x) = 3x - 7
f(c) = 3c - 7
20 = 3c - 7
Add 7
27 = 3c
Divide by 3
9 = c
Answer Choices (Multiple Choice)-
A. 6240+t<=8000
B. 8000>=6240t
C. 6240+5t<=8000
D. 8000+6240<=5t
E. 8000-6240>=5t
Answer:
c,e, d
Step-by-step explanation:
c,e,d is the correct to me
QUESTION 3
(15 marks)
Binomial probability A JHB car Salesman found that 1 out of 5 of consultations result is a sale. If on the
randomly selected day he makes eight 8 consultations what is the probability that he will make.
3. 1 At most, one sale
3. 2 At least one sale
3. 3 Two or three sales
3. 4 Six sales
Using the binomial distribution, it is found that:
3.1 There is a 0.5033 = 50.33% probability that he makes at most one sale.
3.2 There is a 0.8322 = 83.22% probability that he makes at least one sale.
3.3. There is a 0.4404 = 44.04% probability that he makes two or three sales.
3.4. There is a 0.0011 = 0.11% probability that he makes six sales.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
1 out of 5 of consultations result is a sale, hence p = 1/5 = 0.2.8 consultations are considered, hence n = 8.Item 1:
The probability that he makes at most one sale is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.2)^{0}.(0.8)^{8} = 0.1678[/tex]
[tex]P(X = 1) = C_{8,1}.(0.2)^{1}.(0.8)^{7} = 0.3355[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1678 + 0.3355 = 0.5033[/tex]
There is a 0.5033 = 50.33% probability that he makes at most one sale.
Item 2:
The probability that he makes at least one sale is:
P(X > 1) = 1 - P(X = 0) = 1 - 0.1678 = 0.8322.
There is a 0.8322 = 83.22% probability that he makes at least one sale.
Item 3:
The probability that he makes two or three sales is given by:
[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.2)^{2}.(0.8)^{6} = 0.2936[/tex]
[tex]P(X = 3) = C_{8,1}.(0.2)^{3}.(0.8)^{5} = 0.1468[/tex]
Then:
[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3) = 0.2936 + 0.1468 = 0.4404[/tex]
There is a 0.4404 = 44.04% probability that he makes two or three sales.
Item 4:
The probability that he makes six sales is P(X = 6), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{8,6}.(0.2)^{6}.(0.8)^{2} = 0.0011[/tex]
There is a 0.0011 = 0.11% probability that he makes six sales.
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Which proportional line has the smallest slope?
Question 14 options:
y= 8x
y=2x
y= .75x
y=.256x
Answer: y=.256x
Step-by-step explanation:
This line has the smallest coefficient for x.
Question
Find the surface area of the cube.
The surface area is
square yards.
Answer:
81 square yards
Step-by-step explanation:
width- 9 ft
length- 9ft
width times length equals the area which is 81 square feet and if you multiply the height it is 729 which would be the volume.
Hope this helps.
BTW it's my birthday
PLEASE SOLVE THIS I DONT HAVE MUCH TIME I WILL GIVE BRAINLYZ
A rectangle has a length of 10 cm and a width of 6 cm
How long is the diagonal of the rectangle?
Answer:
d = 2√34
Explanation:
d² = 10² + 6²d² = 100 + 36d² = 136d = √136d = 2√34please answer these 3 question
Answer:
i think 5 prisms are cool
Step-by-step explanation:
5% of a number is 80, what is 25% of the same number? A. 4 B. 40 C. 400 D. 440
Answer: 400
Step-by-step explanation:
If 5% of a number is 80, just multiply that number by 5 to get 25 (5 x 5 = 25) and you will get 400.
i am currently struggling to find this algebra 2 answer can anyone help? ill give you whatever
What is 7.23 x 10^5 in standard notation
Delete the comma if needed
================================================
Explanation:
The exponent of 5 means we move the decimal 5 spots to the right.
This has us go from 7.23 to 723,000
If the exponent was negative, then we'd move that amount to the left.
Number 2. Please help!!!!!!!!
Answer:
[tex]\frac{x-3}{x+2}[/tex]
Step-by-step explanation:
[tex]\frac{3x^2+6x-45}{3x^2+21x+30}[/tex] Rewrite
[tex]\frac{x^2+2x-15}{x^2+7x+10}[/tex] Factor out GCF (3)
[tex]\frac{x^2+5x-3x-15}{x^2+5x+2x+10}[/tex] Replace b with factors
[tex]\frac{(x-3)(x+5)}{(x+5)(x+2)}[/tex] Factor by grouping
[tex]\frac{x-3}{x+2}[/tex] Final answer
For a more detailed explanation, please look at the help image attached. It shows each step on how to factor polynomials.
I hope this helps!
In number 1783429 write the follwings:
i)Write rhe digit that is in the ten thousand place.
ii)Successor of the number
Answer:
i) 8
ii) 9
Step-by-step explanation:
For i):
1 = million
7 = hundred thousand
8 = ten thousand place
3 = thousand
4 = hundred
2 = tens (twenty)
1 = unit (one)
For ii):
The successor of a number is the number that comes after the given number. The successor of a given number is 1 more than the given number. Every number has a successor by adding 1 to every number.
For instance, the successor of 0 is 1, the successor of 1 is 2, and so on.
In this case, the successor of 8 is 9 because 8 + 1 = 9
Hope this makes sense. If you need further explanation, let me know.
- profparis
Answer:
i)8
ii)1783429
Step-by-step explanation:
for i, count upto ten thousand and for ii, add 1 to the number
Find the distance between the points.
Answer:
8
Step-by-step explanation:
Answer:
it will be 8
Step-by-step explanation:
A car rental agency has 42 cars (each an identical model). the owner of the agency finds that at a price of $32 per day, all the cars can be rented; however, for each $1 increase in rental cost, one of the cars is not rented. what should the agency charge to maximize income?
Answer:
increase to 38 and have the unused ones in for maintenance
This is a recipe that makes 30 chocolate chip cookies:
- 150g butter
- 160g sugar
- 225g plain flour
- 1 large egg
- 12 teaspoon bicarbonate of soda
- 200g chocolate chips
Miss Watson wants to make 25 cookies for her class.
How much plain flour will she need?
Step-by-step explanation:
30: 225 = 25: X
30/225= 25/X
30×X = 225×25
30X = 5625
X = 187.5
) Neena buys books and puzzles at a yard sale. The price of a book is the same as the price of a puzzle. She spends $15.The situation can be represented by the graph and system of equations shown, where b is the price of each book and p is the price of each puzzle. What is the price of each book? What is the price of each puzzle?
Answer:
Each one 7.50 :)
Step-by-step explanation:
When we add, we can solve this!
7.50 + 7.50 = 15
Have an amazing day!!
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Answer:
Each costs $7.50
Step-by-step explanation:
Given
1 book and 1 puzzle costs $15Both have the same costSolving
If they cost the same, divide the whole cost by the number of items (2)$15/2 = $7.50 [cost of a book/puzzle]The graph of p = 400 and the graph of p = 50s – 200 intersect at the point (12,400). If the equation p = 50s – 200 represents the profit, p, based on s sales, what does the intersection best represent?
a. When the sales are 400, the profit is 12.
b. When the sales are 12, the profit is 400.
c. The profit is always 400.
d. The sales are always 12.
Part A Write a numerical expression to represent the approximate perimeter of triangle FGH in terms of the lengths of its sides.
side FG and FH are 5.8 and side HG is 6 units
p=FG+FH+HG =5.8+5.8+6 is a numerical expression to represent the approximate perimeter of triangle FGH.
Perimeter
The perimeter of a geometric figure is the sum of its sides.
The question gives:
the geometric figure - trianglethe sides of the triangle - 5.8, 5.8 and 6Therefore the perimeter will be the sum of 5.8, 5.8 and 6. You can write as:
p=FG+FH+HG
p= 11.6+6=17.6
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