Answer:
( x+1)^2 = 4
Step-by-step explanation:
x^2+2x-3=0
Add 3 to each side
x^2 +2x = 3
Take the coefficient of x
2
Divide by 2
2/2 =1
Square it
1^2 =1
Add to each side
x^2 +2x = 3
x^2 + 2x+1 = 3+1
( x+1)^2 = 4
Take the square root of each side
x+1 = ±2
Subtract 1 from each side
x+1-1 = -1 ±2
x = -1+2 x = -1-2
x =1 x = -3
help due timed !! help plss
Answer:
290 m
Step-by-step explanation:
3*6*5=90
5*5*8= 200
200+90=290
Recently, More Money 4U offered an annuity that pays 6.3% compounded monthly. If $1,986 is deposited into this annuity every month, how much is in the account after 8 years? How much of this is interest?
Answer:
[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
[tex] I = 3283.153 -1986 = 1297.153[/tex]
Step-by-step explanation:
For this case we can use the formula for the future value using compound interest given by:
[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]
Where P= 1986 the initial amount invested. r = 0.063 represent the interest rate. n=12 represent the number of times that the rate is compounded in a year. And t =8 years . Replacing the info we got:
[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
[tex] I = 3283.153 -1986 = 1297.153[/tex]
A file that is 278 megabytes is being downloaded. If the download is 19.9% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
55.3
Step-by-step explanation:
19.9% of 278 = 55.322
55.322 rounded to the nearest tenth = 55.3
Answer:55.3
Step-by-step explanation:
What is the surface area of the triangular prism?
Triangular prism
a
252 square feet
b
264 square feet
c
152 square feet
d
172 square feet
Answer:
a) 252 square feet
Surface area of triangular prism = 252 square feet
Step-by-step explanation:
Explanation:-
Given diagram Base = 3 feet
Height of the triangular = 4 feet
The slant height of triangular prism 'l' =20 feet
The hypotenuse of the triangle 'c' = 5 feet
prism base area 'p' = h+b+c = = 4 +3+5 =12
Surface area of triangular prism
= [tex]2 (\frac{1}{2} )bh +lA[/tex]
= b h + p l
= 3 ×4 + 12×20
= 252 square feet
Final answer:-
Surface area of triangular prism = 252 square feet
Answer:
252
Step-by-step explanation:
What is the distance between A(-8, 4) and B(4, -1)?
Answer:
10.908
Step-by-step explanation:
what is the name of this 3D shape
Answer:
rectangular prism or cuboid
Step-by-step explanation:
The name of the given 3-D shape is rectangular prism or cuboid
Here is a Fill in the Gaps Question:
A prism is a three-______________ shape with the same _______________ all the way through.
Please help.
Jake :)
P.S you will get 40 pts :)
Answer:
A prism is a three-dimensional shape with the same cross-section all the way through.
Step-by-step explanation: Im not sure if i got the second right
A prism is a three-dimensional shape with the same cross-section all the way through.
A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.
What is called prism?A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve.
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simplify the numerical expression
12-2³
Answer:
12-2³ = 12 - 8 = 4
Hope this helps!
:)
Carl pays $45 per month for car insurance. How much does he spend on car insurance in 1 year?
Answer: 540
Step-by-step explanation: because if he pays 45 bucks a month and a year equals 12 then ya do 45x12 and ya get 540
Answer:
Carl spends $540 per year on car insurance
Step-by-step explanation:
Carl pays $45 per month. There are 12 months in 1 year.
All we need to do is multiply the rate per month by the number of months to get our answer.
[tex]45*12=540[/tex]
if a is a positive number then -a^6 is
Asphere has a radius of 4 in. Which equation finds the volume of the sphere?
Answer:
[tex]V = \frac{4}{3} \pi r^{2}[/tex] - is the formula for the volume of a circle.
Step-by-step explanation:
Step 1:
- Insert your values:
- [tex]V = \frac{4}{3} \pi 4^{2}[/tex]
Step 2:
- Simplify using order of operations:
- Exponents First:
- [tex]V = \frac{4}{3} \pi 64[/tex]
- Division Second:
- [tex]V = 1.333 \pi 64[/tex]
- Multiplication Last:
- [tex]V = 268.01555[/tex]
- And Simplified:
- V = 268 (approx.)
Hope this helps! Good luck!
I have 25 pound bags of cat food . Each serving is 1.8 from the bag. How many servings can you get?
Answer:
10 servings
Step-by-step explanation:
try your best
Answer:
13.8 servings
Step-by-step explanation:
25 divided by 1.8
Two swimmers at opposite ends of a ninety-foot pool start to swim the length of the pool, one at 3 feet per second and the other at 2 feet per second. If they swim back and forth for twelve minutes, how many times do they pass each other?
Answer:
20 times
Step-by-step explanation:
The faster swimmer can swim twice the length of the pool in ...
(2·90 ft)/(3 ft/s) = 60 s
The slower swimmer can do it in ...
(2·90 ft)/(2 ft/s) = 90 s
The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.
A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.
Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.
The swimmers pass each other 20 times in 12 minutes.
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day. The table shows the amount of fiber Jodi has eaten today. How many more grams of fiber does she need to get the recommended daily amount of fiber?
The amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day.
The total amount of fiber Jodi took = 19 + 4 + 2(1) = 25 grams
1 gram = 1000 milligrams
25 grams = 25000 milligrams
The amount of fiber she needs to eat
= 31000 - 25000
= 6000 milligrams
or
= 6 grams
Thus, the amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
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At a costumer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. What is the probability that during a given hour of the day there will be between 146 calls and 163 calls, to the nearest thousandth
We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.
First of all, we will use z-score formula to find z-score corresponding to 146 and 163.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{146-150}{5}[/tex]
[tex]z=\frac{-4}{5}[/tex]
[tex]z=-0.8[/tex]
[tex]z=\frac{163-150}{5}[/tex]
[tex]z=\frac{13}{5}[/tex]
[tex]z=2.6[/tex]
Our next step is to find percentage of data scores falls between both z-scores.
[tex]P(-0.8<z<2.6)=P(z<2.6)-P(z<-0.8)[/tex]
Using normal distribution table, we will get:
[tex]P(-0.8<z<2.6)=0.99534-0.21186[/tex]
[tex]P(-0.8<z<2.6)=0.78348[/tex]
Let us convert our answer into percentage.
[tex]0.78348\times 100\%=78.348\%[/tex]
Upon rounding our answer to nearest thousandths, we will get:
[tex]78.348\%\approx 78.35\%[/tex]
Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately [tex]78.35\%[/tex].
Answer:
0.624
Step-by-step explanation:
DeltaMath
The main span of bridge A is 2500 is percent shorter than the main span of bridge B 4100
Answer:
16%
percentage is calculated by 100
A. 2500 × 1/100 = 25%
B. 4100 x 1/100 = 41%
41% - 25%
16%
therefore bridge A is 16% shorter than bridge B
In ΔIJK, the measure of ∠K=90°, KI = 3.8 feet, and JK = 6.7 feet. Find the measure of ∠I to the nearest degree.
Answer:
60
Step-by-step explanation:tanI=
adjacent
opposite
=
3.8
6.7
\tan I = \frac{6.7}{3.8}
tanI=
3.8
6.7
I=\tan^{-1}(\frac{6.7}{3.8})
I=tan
−1
(
3.8
6.7
)
I=60.44\approx 60^{\circ}
I=60.44≈60
∘
Find the Coordinates of a point A, where AB is diameter of a circle whose
centre is (2,-3) and B is (1,4)
Answer:
(3, -10)
Step-by-step explanation:
let A(x,y) and B(x1,y1)=(1,4)
by midpoint formula i.e. (x+x1)/2 ; (y+y1)/2
as midpoint is centre so,
(2, -3) = (x+1)/2 ; (y+4)/2
2=(x+1)/2 and -3=(y+4)/2
4-1=x and -6-4=y
x=3 and y=-10
therefore A(x,y)=A(3,-10)
Three less than one-fourth of product of eight thirds and nine, write the expression
Answer:
1/4(8/3+9)-3
Step-by-step explanation:
1/4(8/3+9)-3
What’s the value of x?
Answer fast please
So the value of X is 15 degree.
Look at the attached picture
Hope it will help you
Good luck on your assignment
AC=180°
[tex]3x + 8x + 15 = 180 \\ 11x = 165 \\ x = 15[/tex]
The jogging track is 5/9 of a mile long. If Ashley jogged around it four times how far did she run
Answer:
20/9 mile
Step-by-step explanation:
idk pretty self-explanatory
which expression is equivalent p^6)2
So the right answer is p^12.
Look at the attached picture
Hope it will help you
Good luck on your assignment..
Answer:
[tex] {p}^{12} [/tex]
Step-by-step explanation:
[tex]( {p}^{6} ) ^{2} [/tex]
[tex]p ^{6 \times 2} [/tex]
[tex] {p}^{12} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
the base of a expoential function can be a negative number true or false
Answer:
This would be false
Step-by-step explanation:
Exponents can't be negative
Answer:
An exponential function can not be either 1, 0, or any negative number.
What is value of 3x2+4y2if x=2, y=1, and z=-3
Answer:
16
Step-by-step explanation:
3x² + 4y² where x = 2, y = 1, and z = -3
Here we just need to plug in the given values to their respective variables
3(2)² + 4(1)² There are no z variables in this equation so plugging in z = -3 is irrelevant Simplifying our equation we now have: 3(4) + 4(1) = 12 + 4 = 16Answer:
0 if the original expression is : 3x^2 + 4yz
Step-by-step explanation:
3x^2 + 4yz ; I guess this is the original expression.
When x=2, y = 1 z =-3
3x^2 + 4yz = 3(2)^2 + 4 × (1)×(-3)
= 3×4 + 4 × (-3) = 12 - 12 = 0
Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the water level when the water is 6 m deep. (1 L = 1000cm^3)
Answer:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
Step-by-step explanation:
For a tank similar to a cylinder the volume is given by:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:
[tex] \frac{dV}{dt}= \pi r^2 \frac{dh}{dt}[/tex]
And solving for [tex]\frac{dh}{dt}[/tex] we got:
[tex] \frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}[/tex]
We need to convert the rate given into m^3/min and we got:
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
your choices are
Right
Obtuse
Acute
Answer:
obtuseacuteStep-by-step explanation:
Think about a right triangle with legs AB and AC. Then you have ...
AB² +AC² = BC² = 10² = 100
If AB and AC are shorter than that, the sum of their squares will be less than 100. When the legs of a right triangle are shortened, the angle between them must increase in order for them to continue to form a triangle.
The triangle with AB² +AC² < 100 is an obtuse triangle.
__
Conversely, if AB and AC are lengthened so the sum of their squares is greater than 100, the angle between them will have to decrease for them to form a triangle.
The triangle with AB² +AC² > 100 is an acute triangle.
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
What is the probability that all of the sprinklers will operate correctly in a fire?
Answer:
2.82% probability that all of the sprinklers will operate correctly in a fire
Step-by-step explanation:
For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The probability of a sprinkler operating correctly is independent of other sprinklers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.
This means that [tex]p = 0.7[/tex]
10 sprinklers.
This means that [tex]n = 10[/tex]
What is the probability that all of the sprinklers will operate correctly in a fire?
This is P(X = 10).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
2.82% probability that all of the sprinklers will operate correctly in a fire
The probability that all sprinklers will operate correctly in a fire is 0.028
How to determine the probabilityThe given parameters are:
p = 0.7 ---- the probability that a sprinkler to activate correctly
n = 10 --- the number of sprinklers
The probability that all sprinklers activate correctly is calculated as:
[tex]P(10) = p^n[/tex]
So, we have:
[tex]P(10) = 0.7^{10[/tex]
Evaluate
[tex]P(10) = 0.028[/tex]
Hence, the probability that all sprinklers will operate correctly in a fire is 0.028
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Please answer this correctly
Answer:
40 cm.
Step-by-step explanation:
So what I tried to do in this case is compare 96 to 64. I subtracted those two numbers which is 32. So since thats the difference between those two shapes, I did the same thing with 72 and I subtracted it but 32, which led me to 40.
Hope this helped :)
Answer:
u=48
Step-by-step explanation:
In similar triangles, corresponding sides have the same ratio.
64/96=u/72
Step 1: Cross-multiply
(64)*(72)=u*(96)
4608=96u
Step 2: Flip the equation.
96u=4608
Step 3: Divide both sides by 96.
96u /96=4608 /96
u=48
Where do you find your domain restrictions in a rational function?
Answer:
denominator zeros are excluded
Step-by-step explanation:
The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.
The exclusions of interest are generally those values of the variable that make any denominator be zero.
__
Example:
f(x) = (2/(x-3)) / (4/(x -6))
has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...
f(x) = (x -6)/(2(x -3))
but x=6 remains excluded from the domain because of its effect in the original function definition.
_____
Additional comment
If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.
Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.
20% of US High School teens vape. A local High School has implemented campaigns to reduce vaping among students and believes that the percentage of students who vape at this High School is lower than the national average. School administration implements a survey of 300 randomly selected students. They find that 51 of the 300 vape.
If the true proportion of students who vape at this school is 20%, what is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 300, p = 0.2[/tex]
So
[tex]\mu = E(X) = np = 300*0.2 = 60[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282[/tex]
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is [tex]P(X \leq 51 + 0.5) = P(X \leq 51.5)[/tex], which is the pvalue of Z when X = 51.5 So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51.5 - 60}{6.9282}[/tex]
[tex]Z = -1.23[/tex]
[tex]Z = -1.23[/tex] has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300