Answer:
7
Step-by-step explanation:
Simplify the following expression completely.
x2 + 6x + 9
—————-
x2 + 2x - 3
Answer:
The answer is that image below. If it isn't correct, I'm sorry.
A cylidrical container of height 28cm and diameter of 18cm is with water. The water is then poured into another container with a rectangular base of length 27cm and width 11cm . Calculate the depth of the in the container.
Answer:
23.9894949495cm is the depth of the container.
Step-by-step explanation:
Cylindrical container:
height: 28
radius: 9 (or 18/2)
pi * 9² = 254.4690049408
254.4690049408 * 28 = 7,125.1321383424 cm²
cylidrical container area: 7,125.1321383424cm²
Container:
length: 27cm
width: 11cm
27 * 11 = 297
7,125.1321383424 / 297 = 23.9894949495cm
I assume that the container with rectangular base is precisely full when tou pour the water into it.
And that your question was how deep the container was.
factor the polynomial 4x^4-20x^2-3x^2+15 by grouping. what is the resulting expression?
Answer:
(4x^2-3)(x^2-5)
Step-by-step explanation:
We are going to group the first two and last two terms and find the GCF of each set.
4x^4-20x^2-3x^2+15
(4x^4-20x^2)(-3x^2+15)
4x^2(x^2-5)-3(x^2-5)
Then we group the GFCs together and the rest
(4x^2-3)(x^2-5)
What's the solution to 2x – 2 > 2x + 4?
Consider the inequality first ;
[tex]{:\implies \quad \sf 2x-2\> 2x+4}[/tex]
Subtracting 2x from both sides ;
[tex]{:\implies \quad \sf \cancel{2x}-2-\cancel{2x}\> \cancel{2x}+4-\cancel{2x}}[/tex]
[tex]{:\implies \quad \sf -2\> 4}[/tex]
But , as the given situation isn't possible in mathematics , so the inequality have no solutions . Or [tex]{\bf{x\in \phi}}[/tex] , where [tex]\bf \phi[/tex] is the empty set.
Jack draws a pattern of 2 cm wide strips on the wall in the following order: a red strip, a blue strip, an orange strip, a pink strip, and then he repeats the colors in the same order. How long is Jack's pattern if the first and last stripes he painted were red, and he painted six red strips in total?
Answer:
His pattern is 42cm long.
Step-by-step explanation:
Each repetition of the pattern is 8 cm (4 colors time 2cm each)
If the last color is red and he painted 6 red strips in total, then he repeated the pattern 5 times and ended on an extra red strip.
So 8cm times 5 repetitions equals 40, plus 2cm for the extra red strip.
Technology required. Find the missing measurements.
Answer: 40.82
Step-by-step explanation:
Use pythagoras theorem to solve
Root 35 squared + 21 squared = 40.82
How to get -70 from 24/12+72/8-9
Answer:
Step-by-step explanation:
24/12 = 2
72/(8 - 9) Be sure and use brackets when you post a question. 8 - 9 = - 1
72/-1 = - 72
2 - 72 = - 70
Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.
f(n)=n3-7
The first 4 terms of the sequence are______,______,______,_______.
Given:
The given rule is
[tex]f(n)=n^3-7[/tex]
Domain of the function is the set of whole numbers greater than 0.
To find:
The first 4 terms of the sequence.
Solution:
We have,
[tex]f(n)=n^3-7[/tex]
Domain of the function is the set of whole numbers greater than 0. So, the domain for first four terms of the sequence are 1, 2, 3 and 4 respectively.
For n=1,
[tex]f(1)=(1)^3-7[/tex]
[tex]f(1)=1-7[/tex]
[tex]f(1)=-6[/tex]
For n=2,
[tex]f(2)=(2)^3-7[/tex]
[tex]f(2)=8-7[/tex]
[tex]f(2)=1[/tex]
For n=3,
[tex]f(3)=(3)^3-7[/tex]
[tex]f(3)=27-7[/tex]
[tex]f(3)=20[/tex]
For n=4,
[tex]f(4)=(4)^3-7[/tex]
[tex]f(4)=64-7[/tex]
[tex]f(4)=57[/tex]
Therefore, the first 4 terms of the sequence are -6, 1, 20, 57 respectively.
16 - 2t = 3/2 t + 9 .
Answer:
t=2
Step-by-step explanation:
Start by subtracting 9 from both sides. You'll get 7-2t=3/2t. I made 3/2 a mixed number, so 1 1/2. You should have 7-2t=1 1/2t. Add 2t to both sides, because the 2t is negative. You should have 7=3 1/2t. Last step is to divide 3 1/2 into both sides. 7 divided by 3 1/2 is equal to 2, so t=2
3x + y = 16
X + y = 8
What are x and y
Find x-intercept
The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y1=0 and then solve for x.
3x + y = 16
3x + 1(0) = 16
x1 = 5.333 y1 = 0
Find y-intercept
The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.
3x + y = 16
3(0) + y = 16
y2 = 16 x2 = 0
It is generally believed that nearsightedness affects about 15% of all children. A local elementary school registered 120 incoming kindergarteners.
Note that this scenario is talking about a sampling distribution since this school is a sample of size 120. Therefore, you will need to calculate the standard deviation using a formula before using the normalcdf and invNorm commands.
a) What is the mean of the sampling distribution of all samples like this:
b) What is the standard deviation of the sampling distribution of all samples like this:
Give the formula with values that you entered in your calculator as a way of showing your work:
Give your final answer rounded to 4 decimal places:
c) What is the probability that less than 10% of the incoming kindergarteners are nearsighted?
Give the command and values you used as a way of showing your work:
Give your final answer rounded to 4 decimal places:
d) If this school measures at the 80th percentile for all incoming kindergarten classes of size 120, what proportion of incoming kindergarteners are nearsighted?
Give the command and values you used as a way of showing your work:
Give your final answer rounded to 2 decimal places:
Using the normal distribution and the central limit theorem, it is found that:
a) The mean is of 0.15.
b) The standard deviation is of 0.0326.
c) There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.
d) 0.1774 of incoming kindergarteners are nearsighted.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
It is generally believed that nearsightedness affects about 15% of all children, hence p = 0.15.A local elementary school registered 120 incoming kindergarteners, hence n = 120.Item a:
[tex]\mu = p = 0.15[/tex]
The mean is of 0.15.
Item b:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.15(0.85)}{120}} = 0.0326[/tex]
The standard deviation is of 0.0326.
Item c:
The probability is the p-value of Z when X = 0.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1 - 0.15}{0.0326}[/tex]
[tex]Z = -1.53[/tex]
[tex]Z = -1.53[/tex] has a p-value of 0.063.
There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.
Item d:
The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 0.15}{0.0326}[/tex]
[tex]X - 0.15 = 0.84(0.0326)[/tex]
[tex]X = 0.1774[/tex]
0.1774 of incoming kindergarteners are nearsighted.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Please help.
What is 7/8 divided by 6/8
Simplify your answer.
Hey there!
7/8÷6/8=?
Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
7/8×8/6=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
7×8/8×6=56/48
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 56 and 48 using
GCF(56,48) = 8
56÷8/48÷8=76
The fraction
7/6
is the same as
7÷6
Convert to a mixed number using
long division for 7 ÷ 6 = 1R1, so
7/6= [tex]1 \frac{1}{6} [/tex]
Therefore:
7/8÷6/8= 1 1/6
Let's do
[tex]\\ \bf\hookrightarrow \dfrac{7}{8}\div \dfrac{6}{8}[/tex]
[tex]\\ \bf\hookrightarrow \dfrac{7}{8}\times \dfrac{8}{6}[/tex]
[tex]\\ \bf\hookrightarrow \dfrac{7}{8}\times \dfrac{4}{3}[/tex]
Cancel 4 and 8[tex]\\ \bf\hookrightarrow \dfrac{7}{2}\times \dfrac{1}{3}[/tex]
[tex]\\ \bf\hookrightarrow \dfrac{7}{6}[/tex]
One and two step equations
7x-2=-9
Plz asap can y’all explain step by step plzzz it’s for a homework
Answer:
Step 1: Add 2 to both sides.
7x−2+2=−9+2
7x=−7
Step 2: Divide both sides by 7.
7x/7 = -7/7
Answer: x=−1
Answer:
x=-1
Step-by-step explanation:
7x-2=-9 (Given)
7x=-7 (Add 2 on both sides to eliminate he -2 on the left side)
x=-1 (Divide both sides with 7 to eliminate the 7 in 7x)
Answer: x=-1
Angles A and B are supplementary. Angle A has a measure of 80°. What is the measure of angle B?
The measure of angle B is
°.
Answer:
100
Step-by-step explanation:
luke rolls a 10-sided solid with equal-sized faces labeled 1 to 10. what is the probability of rolling a 4?
help giving out 10 points to those who help and the right answer!
1 out of 10, or [tex]\frac{1}{10}[/tex]. It is unlikely to occur.
Tom got 7 over 8 pound of honey from a hive. He calculated the quotient of 7 over 8 ÷ 2 over 5. Which statement shows the quotient and gives the most likely explanation of what Tom was trying to determine?
He can make 14 over 40 of a bottle of honey with 2 over 5 pound of honey in each bottle.
He can get 14 over 40 pound of honey if he divides the honey into 2 over 5-pound portions.
He can get 2 and 3 over 16 pounds of honey if he divides the honey into 2 over 5-pound portions.
He can make 2 and 3 over 16 bottles of honey with 2 over 5 pound of honey in each bottle.
Answer:
D.
Step-by-step explanation:
if he divides (7/8) / (2/5)
he will get x bottles of honey if each bottle weighs 2/5 pound
Kosi traced a rectangle on a coordinate grid. The rectangle had the following vertices: (−6, 5), (2, 5), (2, –1), and (–6, –1). Which of the following numbers are dimensions of the rectangle? Select each correct answer. A. 4 units B. 5 units C. 6 units D. 7 units E. 8 units F. 9 units. help, please!.
Answer:
C) 6 units
E) 8 units
Step-by-step explanation:
Kosi traced a rectangle on a coordinate grid. The rectangle had the following vertices: (−6, 5), (2, 5), (2, –1), and (–6, –1). Which of the following numbers are dimensions of the rectangle? Select each correct answer. A. 4 units B. 5 units C. 6 units D. 7 units E. 8 units F. 9 units. help, please!.
When given vertices for a geometric shapes we find the lengths of the side by using the formula:
When(x1, y1) and (x2, y2)
= √(x2 - x1)² + (y2 - y1)²
A= (−6, 5),B = (2, 5), C = (2, –1), and D = (–6, –1).
For AB
A= (−6, 5),B = (2, 5),
= √(2 -(-6)² + (5 - 5)²
= √8² + 0
= √64
= 8 units
For BC
B = (2, 5), C = (2, –1),.
√(2 - 2)² +(-1 - 5)²
= √0 + -6²
= √36
= 6 units
For CD
C = (2, –1), and D = (–6, –1).
= √(-6 -2)² + (-1 -(-1))²
= √-8² + 0²
= √64
= 8 units
For AD
A= (−6, 5), D = (–6, –1).
= √(-6 -(-6))² + (-1 - 5)²
= √0² + -6²
= √36
= 6 units
Therefore, the following numbers that are dimensions of the rectangle is
C) 6 units
E) 8 units
Solve with explanation please
Answer:
Length of the rectangular lot = 60 meters
Width of the rectangular lot = 30 meters
Step-by-step explanation:
Let the width of the rectangular lot be x meters.
So, Length of the same = 2x metres.
[tex]A(rectangular \:lot) = (2x)(x)[/tex]
[tex]\implies A(rectangular \:lot) = 2x^2[/tex]
When length is increasEd by 40 m and width by 6 m. Then....
New length = [tex](2x + 40) \:m[/tex]
New width =[tex](x + 6) \:m[/tex]
According to the question:
[tex](2x + 40)(x + 6) = 2(2x^2)[/tex]
[tex]\implies 2x(x + 6) + 40(x + 6) - 4x^2=0[/tex]
[tex]\implies 2x^2+12x + 40x + 240 - 4x^2=0[/tex]
[tex]\implies 2x^2- 4x^2+12x + 40x + 240 =0[/tex]
[tex]\implies -2x^2+52x + 240 =0[/tex]
[tex]\implies 2(x^2-26x - 120) =0[/tex]
[tex]\implies x^2-26x - 120=0[/tex]
[tex]\implies x^2-30x+4x - 120=0[/tex]
[tex]\implies x(x-30)+4(x - 30)=0[/tex]
[tex]\implies (x-30)(x+4)=0[/tex]
[tex]\implies x-30=0,\: x+4=0[/tex]
[tex]\implies x=30,\: x=-4[/tex]
Since, x represents the side length, so its value can't be negative.
[tex]\implies x=30[/tex]
[tex]\implies 2x=2(30)=60[/tex]
Thus,
Length of the rectangular lot = 60 meters
Width of the rectangular lot = 30 meters
Bro I have the hardest test Can y’all help me it’s 1+1
Answer:
I think it's 12 bro, I'm not sure
Twice the difference between a number and 10 is equal to 6 times the number 13!
Helpppppppppppppppppl
Answer:
C
Step-by-step explanation:
Rotates then reflects over the y axis.
Answer:
C) rotation, then reflection
Step-by-step explanation:
1. rotates to spot 2. then reflects to spot 3.
Below is an image of 64 = 8 What would the image look like to show 100 ?
Answer: 10 rows of 10
Step-by-step explanation:
How many whole numbers are between 0 and n+7? n is a whole number.
Answer:
At least 7 since 0 is a whole number the lowest n+7 can be is 0+7= 7 and there is seven numbers in between 0 and seven.
Step-by-step explanation:
2/3 of a hippos life is spent underwater, the rest of their life out of water is separated into grazing, sleeping and socialising in the ratio 4:7:1. The average life of a hippo is 45 years, how long will it spend doing each of these activities?
Answer:
Under water is 2/3×45= 30yrs
So rest is 1/3
1/3 is divide in 12 parts
1/3÷12=1/36
Grazing is 4/36×45= 5yrs
Sleeping is 7/36×45=8.75yrs
Socialising is 1/36×45=1.25yrs
A factory made 2400 tools in 30 days.how many tools did it make in one day
Answer:
80 tools in one day
Step-by-step explanation:
30 = 2400
÷ 30
1 = 80
Find the point-slope equation of the line using the point (1,2) and slope of 3/2.
Use the slash key (/) to indicate a fraction.
Answer:
y=3/2 x + 1/2
Step-by-step explanation:
please see attached picture
7th grade help me plzzz
there is more than one question! please help ! i have been struggling all day and today i’m on a time limit !
Answer:
3(5h - 2g)
= 3×5h - 3×2g
= 15h - 6g
5(12g - 4f)
= 5×12g - 5×4f
= 60g - 20f
2(h - 3g)
= 2×h - 2×3g
= 2h - 6g
4(3x - g) + 4x
= 4×3x - 4×g + 4x
= 12x - 4g + 4x
= 16x - 4g
9(4g + 1) - 5g
= 9×4g + 9×1 - 5g
= 36g + 9 - 5g
= 31g + 9
A crate of egg cartons holds 8 cartons
of eggs. Each carton has a dozen
eggs. How many eggs are in 5 crates?
Answer:
480 eggs
Step-by-step explanation:
Given;
A crate of egg cartons holds 8 cartons of eggs.
Each carton has a dozen eggs.
To Find;
How many eggs are in 5 crates?
Note;
Dozen eggs = 12 egg
Solve;
Thus, Dozen eggs × Carton of eggs × many eggs are in crates
→ 12 × 8 × 5
→ 96 × 5
→ = 480
[RevyBreeze]
Write the equation in point slope form of the line that passes through the given point with the given slope (8.7,2.1);5.9