Answer:
A
Step-by-step explanation:
he side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.
Explanation of Cosine 60 = Sine 30
Cosine :
The trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.
Sine :
The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right-angled triangle) to the hypotenuse.
So, these are the reasons :
⇒ The side opposite a 30 degree angle is the same as a side adjacent to 60 degree angle in a right triangle.
⇒ On a unit circle, the y (sin) distance of a 30 degree angle is the same as the x (cos) distance of a 60 degree angle.
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Won has a container with the shape below.
A rectangular prism with length of 18 centimeters, width of 10 centimeters, and height of 12 centimeters. A rectangular pyramid has a base of 18 centimeters by 10 centimeters and height of 10 centimeters.
Which statements are true about the container? Select three options.
The shape can be broken into a rectangular prism and a triangular prism.
The shape can be broken into a rectangular prism and a rectangular pyramid.
The formula for the volume of this figure is V = B h + one-third B h.
The volume of the container is 2,760 centimeters cubed.
The volume of the container is 3,060 centimeters cubed.
Answer:
B. The shape can be broken into a rectangular prism and a rectangular pyramid.
C. The formula for the volume of this figure is V = B h + one-third B h.
D. The volume of the container is 2,760 centimeters cubed.
Step-by-step explanation:
I did the edge test.
Answer:
B, C, ,D
DID HE ES
Step-by-step explanation:
A rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes m it takes for the rock climber to climb 288 feet.
Answer:
The equation is y=12x. It takes 24 minutes for the rock climber to get to 288 feet.
Step-by-step explanation:
Since we know there are 60 minutes in an hour, we can divide 720 by 60. This gives us 12. Therefore, for every minute, the rock climber gets 12 feet higher. Assuming y is the height in feet, and x is the time in minutes, we can create the equation y=12x. Now, to find how long it takes to get to 288 feet, we will substitute y with 288.
288=12x
288/12 = 12x/12
24 = x
Now, we have time in minutes that it takes to get to 288 feet.
Hope this helps!
The equation is y=12x.
It takes 24 minutes for the rock climber to get to 288 feet.
The calculation is as follows:
here we know that
One hour = 60 minutes
so, by dividing 720 from 60 we get 12
here we assume the time in minutes be x
So, the equation is
y = 12x
288=12x
288/12 = 12x/12
24 = x
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Explain when the median of a data set is a better
measure of center than the mean.
Answer:
The median of a data set is better when you have a term or terms that are not close to the other terms
Step-by-step explanation:
For example:
Say you have the data set
1, 15, 17, 18, 22, 84
The median of these terms would be 17.5
(it is the exact center of the data group)
17 + 18 = 35
35/2 = 17.5
The mean of these terms would be 26.17
(this number is not close to the center because the numbers 1 and 84
are not close enough to the other terms)
1 + 15 + 17 + 18 + 22 + 84 = 157
157/6 = 26.17
Answer:
Sample Response: When there is an outlier in the data set, the dot plot or histogram will be skewed. In a skewed representation, the mean is pulled up or down toward the tail of the data. Therefore, skewed data affects the mean more than the median.
What did you include in your response? Check all that apply.
The dot plot or histogram will be skewed.
The mean is pulled up or down toward the tail.
The mean is affected more than the median.
A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m.
With each swing, she travels along an arc that is half as long as the arc of the previous swing.
Which expression gives the total length the monkey swings in her first n swings?
24 divided by .5 or 1/2 (probably .5 tho)
Answer: 24 times 1-.5 divided by .5
Step-by-step explanation:
A factory produces weighted balls to use for exercise by filling spherical rubber shells of different sizes with the sand like material. The materials density is 1.5 grams per centimeter. Assuming the shell weighs 10 grams, what should the balls radius so, when full, it weighs 1 kilogram(or 1000 grams)?
Answer:
r=5.4
As mentioned above, the actual \goldE{\text{total quantity}}total quantitystart color #a75a05, start text, t, o, t, a, l, space, q, u, a, n, t, i, t, y, end text, end color #a75a05 is 1000-10=\goldE{990}1000−10=9901000, minus, 10, equals, start color #a75a05, 990, end color #a75a05 grams, since we are trying to find the volume of the air within the shell.
Let's denote the ball's radius as rrr. Then, the \maroonD{\text{volume}}volumestart color #ca337c, start text, v, o, l, u, m, e, end text, end color #ca337c is \maroonD{\dfrac43\pi r^3}
3
4
πr
3
start color #ca337c, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, end color #ca337c.
Now we can plug \blueE{\text{density}=1.5}density=1.5start color #0c7f99, start text, d, e, n, s, i, t, y, end text, equals, 1, point, 5, end color #0c7f99, \goldE{\text{total quantity}=990}total quantity=990start color #a75a05, start text, t, o, t, a, l, space, q, u, a, n, t, i, t, y, end text, equals, 990, end color #a75a05, and \maroonD{\text{volume}=\dfrac43\pi r^3}volume=
3
4
πr
3
start color #ca337c, start text, v, o, l, u, m, e, end text, equals, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, end color #ca337c in the equation.
Sara creates a box plot using 23, 26, 44, 19, 31, 39, and 43 as the data. Which of the following box plots shows the data accurately?
The box plots show the data accurately is the 3rd box (the one with a median line equal 31).
How to find the median data?Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong a same number of observations.
To identify the correct box plot it is enough to calculate the median value from the given set of data.
When we arranged the data set of all the numbers, we can easily spot which one is in the middle (median):
19, 23, 26, 31, 39, 43, 44
Here we can see that 31 is the median.
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If the sales tax is 7% on all purchases, how much must you set aside for sales tax on $300? Show your work.
Answer:
$321
Step-by-step explanation:
Because if you use a calculator u put in 300 + 7% you get 321
Answer: $8.04
Step-by-step explanation: First you add on 7% to all of the amounts, then you get the new answer and subtract it by the old answer, finally you add up the subtracted amounts together. (Sorry if its wrong it tried my best)
In the image shown, line n is a transversal cutting parallel lines l and m.
∠1 = x + 40
∠5 = 2x + 10
What is the measure of ∠5?
A) 65°
B) 67°
C) 70°
D) 72°
Answer:
it is 70 on usatestprep.
Step-by-step explanation:
x + 40 = 2x + 10
x = 30
So, ∠5 = 2x + 10 = 2(30) + 10 = 70
Answer:
The answer is C.) 70
Step-by-step explanation:
Corresponding angles are congruent. So, set the angles equal to each other and solve for x.
x + 40 = 2x + 10
x = 30
So, ∠5 = 2x + 10 = 2(30) + 10 = 70°
2. Ms. Bever has one roll of toilet paper with 500 sheets. How many days will the roll of toilet
paper last if she uses 5 sheets of toilet paper every time she uses the washroom. One the
average day, Ms. Bever uses the washroom 6 times. How many days will she have toilet paper
for?
Answer: 30 days
Step-by-step explanation: 5 x 6 = 30 and she has 500 sheets it would take her about 30 days
Ms. Bever uses 30 sheets of toilet paper per day. A roll of 500 sheets would last her approximately 16.67 days, which means it will last for 16 full days.
Ms. Bever uses 30 sheets of toilet paper per day since she uses the washroom 6 times and uses 5 sheets each time (5 sheets * 6 uses = 30 sheets per day).
To find out how many days a roll will last, we will calculate the number of total sheets divided by the sheets used per day. So, with a roll of 500 sheets, the calculation is 500 sheets / 30 sheets per day = approximately 16.67 days.
Since Ms. Bever cannot use two-thirds of a sheet, the toilet paper will last for 16 full days, with some extra sheets left over which aren't sufficient for another full day of use.
When determining which x-values would make an expression undefined, you do not need to include the factors you canceled out.
True or false?
I think it’s false, but I’m not confident in my answer
Answer:
This is truly false.
When determining which x-values would make an expression undefined, you do need to include the factors you canceled out.
Step-by-step explanation:
When working with functions, it is said to be undefined when the value of the function doesn't take on a value, and this occurs when the denominator is equal to 0.
Take for example
(x-2)/(x-2)
This simple function can be simplifted further by cancelling out the factors to get 1, but that doesn't change the fact that, at x=1, this function becomes undefined.
Because, the values of x can vary and can take on values that can make the denominator to be 0, factors that are cancelled need to be included in checking for where a function is undefined.
Hope this Helps!!!!
A college has a student to teacher ratio of 30 to 2. If there are 186 teachers at the college, how many students attend the college?
Answer:
2790 college students
Step-by-step explanation:
30 to 2
15 to 1
186 times 15
equals 2790 students
Which of the following are possible equations of a parabola that has no real solutions and opens downward?
y > = -(x + 4)^2- 2
y > = -(x + 4)^2 + 2
y > = -x^2 - 2
y > = (x - 4)^2 + 2
y > = -(x - 4)^2- 2
Answer:
[tex]y = - {(x - 4)}^{2} - 2[/tex]
[tex]y = - {(x + 4)}^{2} - 2[/tex]
[tex]y = - {x}^{2} - 2[/tex]
Step-by-step explanation:
A vertex form equation of a parabola is of the form
[tex]y = a(x - h)^{2} + k[/tex]
with vertex at (h,k).
If a parabola opens downwards, then a<0.
If the vertex of such parabola is below the x-axis, then it has no real solution, because it will not intersect the x-axis.
[tex]y = - {(x + 4)}^{2} - 2[/tex]
has vertex at (-4,-2), which is below x-axis.
[tex]y = - {(x - 4)}^{2} + 2[/tex]
has vertex at (-4,2)--->above x-axis
[tex]y = - {(x - 4)}^{2} - 2[/tex]
vertex at (4,-2) ---> below x-axis
[tex]y = - {x }^{2} - 2[/tex]
(0,-2)----> below x-axis
The mean percent of childhood asthma prevalence in 43 cities is 2.23%. A random sample of 31 of these cities is selected. What is the probability that the
mean childhood asthma prevalence for the sample is greater than 2.6%? Interpret this probability. Assume that o = 1.24%.
The probability is
(Round to four decimal places as needed.)
Given Information:
Mean percent of childhood asthma = μ = 2.23%
Sample size = n = 31
Standard deviation = σ = 1.24%
Required Information:
P(X > 2.6) = ?
Answer:
P(X > 2.6) = 0.0475 = 4.75%
Step-by-step explanation:
Let X is the random variable that represents percent of childhood asthma prevalence.
We want to find out the probability that the mean childhood asthma prevalence for the sample is greater than 2.6%
[tex]P(X > 2.6) = 1 - P(X < 2.6)\\\\P(X > 2.6) = 1 - P(Z < \frac{x - \mu}{\frac{\sigma}{\sqrt{n} } } )\\\\P(X > 2.6) = 1 - P(Z < \frac{2.6 - 2.23}{\frac{1.24}{\sqrt{31} } } )\\\\P(X > 2.6) = 1 - P(Z < \frac{2.6 - 2.23}{0.222} )\\\\P(X > 2.6) = 1 - P(Z < \frac{0.37}{0.222} )\\\\P(X > 2.6) = 1 - P(Z < 1.67)\\[/tex]
The z-score corresponding to 1.67 is 0.9525
P(X > 2.6) = 1 - 0.9525
P(X > 2.6) = 0.0475
P(X > 2.6) = 4.75%
Therefore, there is 4.75% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.6)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.67 then go for 0.07 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Using the normal distribution and the central limit theorem, it is found that that there is a:
0.0485 = 4.85% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%. The interpretation is that when many samples of 31 are chosen, around 4.85% of them will have an asthma prevalence greater than 2.6%.
---------------------------------
When the distribution is normal, the z-score formula is used, with [tex]\mu[/tex] as the mean and [tex]\sigma[/tex] as the standard deviation.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. Each z-score has a p-value associated with it.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. For a sample of n observations, by the Central Limit Theorem, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]---------------------------------
Mean of 2.23% means that [tex]\mu = 2.23[/tex]Standard deviation of 1.24% means that [tex]\sigma = 1.24[/tex]Sample of 31 means that [tex]n = 31, s = \frac{1.24}{\sqrt{31}} = 0.2227[/tex]---------------------------------
The probability of a sample mean above 2.6% is 1 subtracted by the p-value of Z when X = 2.6. Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.6 - 2.23}{0.2227}[/tex]
[tex]Z = 1.66[/tex]
[tex]Z = 1.66[/tex] has a p-value of 0.9515.
1 - 0.9515 = 0.0485.
0.0485 = 4.85% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%. The interpretation is that when many samples of 31 are chosen, around 4.85% of them will have an asthma prevalence greater than 2.6%.
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Which scatterplot would have a trend line with a negative slope
Answer: B
Step-by-step explanation:
Answer: B
What is an example of a negative slope?
For example, as more people quit smoking (x), fewer people develop lung cancer (y). The graph for this relationship has a negative slope. If the gradient is negative, then the gradient and the gradient must be opposite, one must be positive and the other must be negative.
In other words, you go up and down or left and right. The positive area of a function is the interval at which the function is on the x-axis. Where the y value is positive (not zero). The negative area of a function is the interval at which the function is below the x-axis.
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Adele's grandmother is 56 years older than she is. Let a represent Adele's age . Write an expression for Adele's grandmother's age.
THIS IS DUE TODAY PLEASE HELP ME OUT!!!!!
Answer:
B
Step-by-step explanation:
It is linear because x+15 is how the number increases. It does not tremendously add up.
Malachi bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. A sales tax of 3% is applied to the discounted total. What was the sale price with tax of Malachi’s fishing rod to the nearest cent? *
Answer:
110.30
Step-by-step explanation:
125.99-(125.99X0.15)= 107.09
107.09+(107.09X0.03)= 110.30
Please answer ASAP! Can someone help? 25 points! Please show your work!
A diameter of a circle has endpoints P(-10, -2) and Q(4, 6).
a. Find the center of the circle.
b. Find the radius. If your answer is not an integer, express it in radical form.
c. Write an equation for the circle
Gabriel makes a model of a pyramid with the dimensions shown. A square pyramid. The square base has side lengths of 12 inches. The triangular sides have a height of 11 inches. Gabriel wants to paint the model. How much paint will he need? The area of the square base is in.2. The area of each triangular face is in.2. Gabriel will need in.2 of paint.
Answer:
The area of the square base is 114 in. 2
The area of each triangular face is 66 in. 2
Gabriel will need 408 in. 2 of paint
Kaden makes 2 cups of salsa for a party. The 6 guests share the salsa equally. Write a fraction that shows how much each guest eats.
Answer:
1/6
Step-by-step explanation:
if it's split equally between 6 people then each gets 1/6
Final answer:
Each guest at the party would get ⅓ cup of salsa.
Explanation:
Kaden makes 2 cups of salsa for a party and the 6 guests share the salsa equally. To determine how much each guest eats, we divide the total amount of salsa by the number of guests. We perform the following calculation:
Total amount of salsa: 2 cupsNumber of guests: 6We divide the total cups of salsa, which is 2, by the number of guests, which is 6:
2 cups ÷ 6 guests = ⅓ cup per guest
Therefore, the fraction that shows how much each guest eats is ⅓ cup.
write down the expression for the nth term of the following sequence 7,16,25,34,43 the following patterns are made using small squares write down an expression forthe number of small squares in pattern n
Final answer:
The nth term of the sequence 7, 16, 25, 34, 43 is found using the arithmetic sequence formula and is 9n - 2. The number of small squares in pattern n is expressed as n².
Explanation:
The given sequence 7, 16, 25, 34, 43 is an arithmetic sequence, where each term increases by 9. To find the expression for the nth term, we use the formula for the nth term of an arithmetic sequence, which is an = a₁ + (n-1)d, where a1 is the first term and d is the common difference. In this case, a1 = 7 and d = 9, so the nth term expression would be an = 7 + (n-1)9 = 9n - 2.
For the number of small squares in pattern n, if the expression given is n², it suggests the number of squares grows quadratically with the pattern number. Therefore, the expression for the number of small squares in the nth pattern would be n².
4. Which two numbers have an absolute value of 2.67?
Answer:
2.67 & -2.67 both have an absolute value of 2.67
Step-by-step explanation:
The absolute value is the distance between a number and zero. the distance between 2.67 and zero is 2.67, and the distance between -2.67 and zero is also 2.67.
Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 71^\circ$, $\angle STU = 36^\circ$, and $\angle TUS = 73^\circ$, then what is $\angle NZM + \angle NPM$ in degrees?
Answer:
<NPM + <NZM = 146°
Step-by-step explanation:
Given:
In triangle STU: M, N and P are the midpoints of the line TU, US and ST respectively.
Line UZ is the altitude of the triangle STU
<TSU =71°, <TSU = 36°, <TUS = 73°
From the diagram:
N is the midpoint of line SU and M is the mid point of line UT.
∴ Line NM is parallel to line ST
P is the mid point of line ST and M is the mid point of line UT
∴Line PM is parallel to line SU
N is the mid point of line SU and P is the mid point of line ST
∴Line NP is parallel to line UT
Δ SPN = Δ STU = 36°
<SPN + <NPM + <MPT (Sum of angles in a triangle = 180°)
<UST = <MPT = 71°
36° + <NPM + 71° = 180°
<NPM + 107° = 180°
<NPM= 180°-107°
<NPM= 73°
In ΔSNZ, line SN = line NZ
∴ side SN = side NZ
< NSZ = <NZS = 71°
<MTZ = <MZT = 36°
<NZS + <NZM <MZT = 180° (Sum of angles in a triangle = 180°)
71° + <NZM + 36° = 180°
107° + <NZM = 180°
<NZM = 180° - 107°
<NZM = 73°
<NPM + <NZM =73° + 73°
<NPM + <NZM = 146°
If A represents the number of pencils in a pack, which expression represents 6 packs of pencils?
A +6
A-6
Ax6
A6
Answer:
Ax6
Step-by-step explanation:
For example, If you had 2 pencils in a pack and there were 6 packs of pencils. You would do 6 times 2 to find out how many pencils you have in total. In other words, you do A times 6.
Suppose that a Navy submarine is submerged 500 feet below sea level.
Answer:
B) A and D
Step-by-step explanation:
Below sea level already implies negative.
And on a number line, it should be -500
Te game started at 7:50pm. It ended at
10:04pm. How long was the game?
Answer:
134 minutes or 2 hours and 14 minutes
Step-by-step explanation:
Answer:
2 hours and 14 minutes
Step-by-step explanation:
What is the prime factorization for 160 using exponents?
Answer:
[tex]2^5*5[/tex]
Step-by-step explanation:
Step 1: Prime Factorization
[tex]160[/tex] → [tex]2 * 2 * 2 * 2 * 2 * 5[/tex]
[tex]2 * 2 * 2 * 2 * 2 * 5[/tex] → [tex]2^5*5[/tex]
Answer: [tex]2^5*5[/tex]
6 x to the 3 fourths power in radical form? (1 point) Question 3 options: 1) cubed root of 6 x to the fourth power 2) fourth root of 6 x cubed 3) 6 cubed root of x to the fourth power 4) 6 fourth root of x cubed
Answer:4) 6 fourth root of x cubed
Step-by-step explanation:
what is the constant term in the expression 24xy -5yz + 82z - 62
[tex]\text{The constant term is the term that doesn't have a variable in it}\\\\\text{As you can see in the expression 24xy -5yz + 82z - 62, the only term}\\\text{that doesn't have a variable is -62}\\\\\text{This means that -62 would be your constant term}\\\\\boxed{\text{Constant term: -62}}[/tex]
A storage shed in the shape of a cube has a height of 12 ft. There are 16 identical cube-shaped boxes in the shed. The edge of each box is 2.5 ft. How much space is left in the shed?
There are____ cubic feet left in the shed.
Answer:
576
Step-by-step explanation:
Answer:
1478ft³
Step-by-step explanation:
12x12x12=1728 ft³
16(2.5x2.5x2.5)= 250ft³
1728-250=1478ft³
There are 1478ft³ left in the shed