Answer:
x = 25
Step-by-step explanation:
The two angles form a straight line so they add to 180
5x-5 + 2x+10 = 180
Combine like terms
7x +5 = 180
Subtract 5 from each side
7x+5-5 = 180-5
7x = 175
Divide by 7
7x/7 = 175/7
x = 25
Answer:
the value of x = 25
Step-by-step explanation:
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Use the given values of n= 93 and p= 0.24 to find the minimum value that is not significantly low, μ- 2σ , and the maximum value that is not significantly high, μ+2σ. Round your answer to the nearest hundredth as needed.
a. Minimum: 30.56; maximum: 14.08
b. Minimum: 14.08; maximum: 30.56
c. Minimum: 18.2; maximum: 26.44
d. Minimum:-11.61; maximum: 56.25
Answer:
The answer is "Option a".
Step-by-step explanation:
[tex]n= 93 \\\\p= 0.24\\\\\mu=?\\\\ \sigma=?\\\\[/tex]
Using the binomial distribution: [tex]\mu = n\times p = 93 \times 0.24 = 22.32\\\\\sigma = \sqrt{n \times p \times (1-p)}=\sqrt{93 \times 0.24 \times (1-0.24)}=4.1186[/tex]
In this the maximum value which is significantly low, [tex]\mu-2\sigma[/tex], and the minimum value which is significantly high, [tex]\mu+2\sigma[/tex], that is equal to:
[tex]\mu-2\sigma = 22.32 - 2(4.1186) = 14.0828 \approx 14.08\\\\\mu+2\sigma = 22.32 + 2(4.1186) = 30.5572 \approx 30.56[/tex]
I need help with this
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JK=8x+6 KL=6x+20 find JL
Answer:
14x + 26
Step-by-step explanation:
JL = JK + KL
= 8x + 6 + 6x + 20
= 8x + 6x + 6 + 20
JL = 14x + 26
In forming a confidence interval for μ1 - μ2, only two assumptions are required: independent samples and sample sizes of at least 30.
a. True
b. False
Miller's Steakhouse offers 8 side dishes, 5 types of steak, and 4 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 3 different toppings and 3 different side dishes?
Answer:
1120
Step-by-step explanation:
To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.
Josue leans a 26-foot ladder against a wall so that it forms an
angle of 80° with the ground. How high up the wall does the
ladder reach? Round your answer to the nearest hundredth of a
foot if necessary.
Answer:
25.61 feet
Step-by-step explanation:
First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.
Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.
One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have
sin(80°) = opposite / 26 feet
multiply both sides by 26 feet
sin(80°) * 26 feet = opposite
= 25.61 feet as the height of the wall the ladder reaches
The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.
The condition is shown in the diagram.
Then the height of the wall will be
[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]
More about the right-angle triangle link is given below.
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Combine the expressions below
4x+(-2x)+6+(-9)
=4x-2x=2x
=6-9=-3
=2x-3
Engineering
When p= 3, q. I and r. 2, the
expression 2p² q3 is equal to
Answer:
[tex]{ \tt{2 {p}^{2} {q}^{3} }} \\ = { \tt{ {2(3)}^{2} . {(1)}^{3} }} \\ = 18[/tex]
Each pizza shown is broken up into different sized slices, but they are all equivalent.
Come up with another ratio of pizza slices that is equivalent to all of these pizzas.
Consider the equation 2x-8=10-x. Why can't you determine whether this equation is true or false?
Answer:
False
Step-by-step explanation:
If we consider x=1 then
2*1-8 = 10-1
2-8 =9
6 = 9 (which is impossible)
so false
We can determine that the original equation 2x - 8 = 10 - x is true when x = 6.
We have,
Simplify the equation:
2x - 8 = 10 - x
Combining like terms by adding x to both sides:
3x - 8 = 10
Now, to isolate the variable x, add 8 to both sides:
3x = 18
Finally, divide both sides of the equation by 3:
x = 6
By solving the equation, x = 6.
Therefore,
We can determine that the original equation 2x - 8 = 10 - x is true when x = 6.
Learn more about equations here:
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The travel time on a section of a Long Island Expressway (LIE) is normally distributed with a mean of 80 seconds and a standard deviation of 6 seconds. What travel time separates the top 2.5% of the travel times from the rest
Answer:
The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 80 seconds and a standard deviation of 6 seconds.
This means that [tex]\mu = 80, \sigma = 6[/tex]
What travel time separates the top 2.5% of the travel times from the rest?
This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 80}{6}[/tex]
[tex]X - 80 = 6*1.96[/tex]
[tex]X = 91.76[/tex]
The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
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if p is a acute angle then p is how many degrees
Answer:
Less than 90⁰
Step-by-step explaination:
If p is an acute angle then, p can be equal to any measurement less than 90⁰
It can be upto 89⁰
Answer:
0 < angle < 90
Step-by-step explanation:
Acute angles are between 0 and up to 90 degrees
Right angles are 90 degrees
Obtuse angles are greater than 90 degrees and less than 180 degrees
During a sale, CDs that normally cost $6.98 each were priced at 2 for $12.50. Pete bought 4 CDs at the sale price. How much money did he save by buying the 4 CDs on sale?
Answer:
2.92
Step-by-step explanation:
Normal price
4 * 6.98 =27.92
Sale price
2 for 12.50 means 4 at 2* 12.50
2*12.50 = 25
Subtract
27.92-25=2.92
He saved 2.92
Each spring, Bill's yard has about 950 square feet of space to cover with mulch. One year, trying to save some cash, Bill bought cheapo overseas mulch from a gas station, and the packaging said that each bag covered 1.8 square meters. How many bags did Bill need
Answer:
161 bags
Step-by-step explanation:
Since we need to know how many square feet a bag can cover, we need to convert the 1.8 square meters to feet. A meter is about 3 feet and 3.5 inches, so to find how many bags he needs we need to convert the bag into feet. First lets convert the meter into inches:
[tex](3*12)+3.5\\(36)+3.5 = 39.5[/tex]
Remember that a foot is 12 inches. Now, we need to multiply the 39.5 inches by 1.8 to find out how many square inches a bag holds.
[tex]39.5*1.8 = 71.1[/tex]
We need square feet though, so let's divide our 71.1 inches by 12 to get a foot measurement.
[tex]71.1/12=5.93[/tex]
A bag holds 5.93 square feet of mulch. Now, to figure out how many bags he needs, we need to divide 950 (total area to cover) by 5.93 (area each bag covers).
[tex]950/5.93=160.2[/tex]
Since Bill cant buy a fifth of a bag, we need to round up so he has enough. So, Bill needs 161 bags of mulch to cover his yard.
3y+5 < 10
solve for y
Answer:
y>3/5
Step-by-step explanation:
3y+5 <10
3y<5
y>3/5
Answer:
[tex]\:3y+5<10\\3y+5-5<10-5\\3y<5\\\frac{3y}{3}<\frac{5}{3}\\y<\frac{5}{3}[/tex]
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G. Find the ratio between a pen and pencil if ten pens cost $22.5 and a dozen pencils cost $18.
Answer:
Cost ratio of pens:pencils = 9 : 4
Step-by-step explanation:
Pen : Pencil
10/10 : 12/12
22.5 / 10 : 18 / 12
2.25 : 1.5 cost per pen : pencil
HC of 0.25 and 0.5 is 8
8 x 2.25 = 18:
1.5 x 8 = 12
Then place them under their denominator x 10 x 12
pens = 18/10 = 1.8
pencils = 12/12 = 1
HC of 1.8 and 1 is 5
1.8 x 5 = 9
1 x 5 = 5
Answer = 9 : 4
Зу = -2 - 6
3y = 2z - 6
Answer:
y = -8/3, z = -1
!!! I need help with this question !!! I tried using the standard deviation formula but my answers are wrong. Can someone please help me! Thank you for your help!
Answer:
Step-by-step explanation:
Not sure how to do this
What is the value of x in the equation
-%y = 30, when y = 15?
Answer:
x not given
therefore no answer for x
the length of a rectangle is twice its width the perimeter is 48 cm what are the dimensions of the rectangle
Answer:
The length=16cm and the width=8cm.
Step-by-step explanation:
Given that the length is twice the breadth or width of the rectangle
Let's assume that the breadth of the rectangle is x.
Thus the length is 2x.
Given perimeter=48cm
The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.
2(x+2x)=48
(3x)=48/2
3x=24
x=8cm
2x=16cm
Step-by-step explanation:
length=2x
width=x
2x+x+2x+x=48
6x=48
6x÷6=48÷6
x=8
length=16
width=8
Two parallel lines are cut by a transversal. What is the measure of 1
Both lines are parallel so using the bottom line you are given angle 7 as being 80 degrees. Angle 5 and 7 form a straight line which is 180 degrees so angle 5 would be 180-80 = 100 degrees.
Angle 1 is the same as angle 5 so angle 1 is 100 degrees.
Answer: 100 degrees
Answer:
B. 100°
Step-by-step explanation:
Angles 1 and 5 are corresponding angles and congruent.
Angles 5 and 7 are a linear pair and supplementary angles, so their measures add to 180°.
m<5 + m<7 = 180°
m<5 + 80° = 180°
m<5 = 100°
m>1 = m<5
m<1 = 100°
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
44.5 units squared
Step-by-step explanation:
First, separate the figure into two different shapes. You should get a rectangle and a triangle after doing this. Next, we'll work on the rectangle. Multiply 2 by 10, and you'll get the area of the rectangle, which would be 20 units squared. We can't multiply 3 by 2, as that would cause the triangle to have 4 sides rather than 3. A triangle can ONLY have 3 sides anyway, so always remember that. Next, we'll work on the triangle. Subtract 10 by 3, and you'll get 7. This will be the triangle's height, so the equation would be 7 X 7 divided by 2, which would be 24.5 units squared. Finally, add 24.5 and 20. You should get 44.5 units squared as your final answer.
So, the final answer for this problem would be 44.5 units squared.
Hope this helped!
Solve the equation below through elimination. -3x-3y=3 -5x+2y=19
HOW TO SOLVE SYSTEMS OF EQUATIONS BY ELIMINATION
To solve systems of equations by elimination, we want to eliminate one of the variables. To do this, we want to cancel out a certain variable in both equations. For example, if you had 8x in one equation and -8 x in another, you could combine the two equations and the x would be gone!
THE SOLUTION
In our case, though, we don't have anything we can combine to cancel out the variables. But, what we can do is multiply the first equation by three. If we do this, now we have a 9x in the top and a -9x in the bottom. Then, we can solve for y!
SOLVING FOR Y
Multiply first equation by three
9x+6y=57
Combine top and bottom equations
14y=28
We divide both sides by 14.
y=2
SOLVING FOR X
Now, we can simply plug our y-value into one of the original equations and then solve for x.
3x+4=19
We subtract 28 from both sides.
3x=15
We divide both sides by 3.
x=5
Therefore, our solution is (5,2) or x=5 and y=2.
I hope that this helps! Have a wonderful day! :D
Answer:
x=5 and y=2.
Step-by-step explanation:
15
Simplify
a
25
O A. a3
O B. a10
O c. a-10
O D. a-3
Answer:
B is the correct answer of your question.
I HOPE I HELP YOU....
The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the diameter is13cm. (Round your answer to three decimal places if required)
Answer:
Step-by-step explanation:
This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.
We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of
[tex]S=4\pi r^2[/tex]
In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that
d = 2r so
[tex]\frac{d}{2}=r[/tex] Now we can have the equation in terms of diameter instead of radius. Rewriting:
[tex]S=4\pi(\frac{d}{2})^2[/tex] which simplifies to
[tex]S=4\pi(\frac{d^2}{4})[/tex] and a bit more to
[tex]S=\pi d^2[/tex] (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.
[tex]\frac{dS}{dt}=\pi*2d\frac{dD}{dt}[/tex] Now let's look at the problem and see what we are given as far as information.
The rate at which the surface area changes is -3.8, and we are looking for [tex]\frac{dD}{dt}[/tex], the rate at which the diameter is changing, when the diameter is 13. Filling in:
[tex]-3.8=\pi(2)(13)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]-\frac{3.8}{26\pi}=\frac{dD}{dt}[/tex] and divide to get
[tex]\frac{dD}{dt}=-.459\frac{cm}{min}[/tex] Obviously, the negative means that the diameter is decreasing.
what is the length, in units, of CD.
As you can see in the image I already got it correct but I kind of guessed. I want to know how to properly solve this without using sin, cos, and tangent functions since this unit has not yet covered those nor are we supposed to know them.
Answer:
I hope D option is write
I hope you help
Which of the following is equal to -18
Step-by-step explanation:
9i√2
-18
so therefore the answer is 9i√2
What is the value of the expression 10(6 + 5)² when b = 3?
10(3+5)^2
10(8)^2
10(64)
=640