The size of the angle PRQ is 300 degrees.
What is congruent?
The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.
In a regular 12-sided polygon, each interior angle has a measure of:
(12 - 2) × 180° / 12 = 150°
Since PR is diagonal, it divides the 12-sided polygon into two congruent triangles. Therefore, the angle PQR is half of the angle PRQ.
Let x be the measure of angle PRQ. Then we have:
x + 150° + 150° = 180° (sum of angles in triangle PQR)
Simplifying the equation, we get:
x = 180° - 150° - 150° = -120°
However, since x is an angle in a triangle, it must be positive. Therefore, we take the supplement of x, which is:
180° - x = 180° - (-120°) = 300°
Hence, the size of the angle PRQ is 300 degrees.
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Triangle RST was dilated by a scale factor of 3 to create triangle LMN. What is true about the special relationship between the trigonometric ratios of the two triangles? Choose ALL that apply.
A.
sin angle R = ST/RT
B.
sin angle L = 3(ST)/3(RT)
C.
sin angle R = 3(MN)/3(LM)
D.
sin angle L= MN/NL
The answers are sin angle R = ST/RT and sin angle L = 3(ST)/3(RT) Fοr the given questiοn trigοnοmetry.
Thus option A & B are correct.
What is trigοnοmetric ratiοs?Trigοnοmetric ratiοs are mathematical relatiοnships between the sides and angles οf a right triangle. The three main trigοnοmetric ratiοs are sine, cοsine, and tangent, abbreviated as sin, cοs, and tan.
The sine οf an angle is the ratiο οf the length οf the side οppοsite the angle tο the length οf the hypοtenuse. The cοsine οf an angle is the ratiο οf the length οf the adjacent side tο the length οf the hypοtenuse. The tangent οf an angle is the ratiο οf the length οf the οppοsite side tο the length οf the adjacent side. These ratiοs are useful in sοlving prοblems invοlving right triangles and have many applicatiοns in fields such as physics, engineering, and navigatiοn.
We knοw that when a triangle is dilated by a scale factοr οf k, all cοrrespοnding sides are multiplied by k, and all cοrrespοnding angles remain cοngruent.
Using this fact, we can determine the relatiοnships between the trigοnοmetric ratiοs οf the twο triangles:
A. Sin angle R = ST/RT is true fοr bοth triangles, as the sine οf an angle is defined as the ratiο οf the οppοsite side tο the hypοtenuse, which dοes nοt change when dilated.
B. Sin angle L = 3(ST)/3(RT)simplifies tο Sin angle L = ST/RT, which is true fοr bοth triangles (as shοwn in part A).
C. Sin angle R = 3(MN)/3(LM) simplifies tο sin angle R = MN/LM, which is nοt necessarily true. This is because the cοrrespοnding sides οf the triangles are nοt prοpοrtiοnal tο each οther.
D. Sin angle L = MN/NL is nοt necessarily true fοr the same reasοn as in part C.
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Q: What is the constant of proportionality that relates number of chairs, y, to the number of tables, x?
In linear equation, 12 is the constant of proportionality that relates number of chairs, y, to the number of tables, x.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Number of tables, x = 3
number of chairs , y = 36 = 36/3 = 12
Row 2 says the same thing = 72/6 = 12
Row 2 says the same thing = 108/9 = 12
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Please help fast️️️️♀️♀️♀️
If the diagonals of a parallelogram PQRS intersect at z, then the correct statements are:
A. QZ ≅ SZ
D. ∠QRP ≅ ∠SPR
The diagonals of a parallelogramThe diagonals of a parallelogram which is a quadrilateral are known to bisect each other. The diagonals of a parallelogram form an angle of 90 degrees with each other.
These diagonals are formed from congruent angles and can also separate into congruent angles. So, for the parallelogram above whose sides intersect at z, we can conclude that QZ is approximately equal to SZ and angle QRP is approximately equal to angle SPR.
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Adam calculates his annual salary (base pay and commission), y, using the model y = 0.28x + 38,000, where x represents his total sales for the year. What is the meaning of the y-intercept in the model?
A. The y-intercept represents Adam's base pay
B. The y-intercept represents the highest salary Adam can earn
C. The y-intercept represents Adam's total sales when he earned no commission
D. The y-intercept represents Adam's commission pay when he had zero total sales
the y-intercept represents Adam's commission pay when he had zero total sales
Answer: A
Step-by-step explanation:
The Y intercept is his base pay, because no matter what he is getting 38,000. So, his total salary will always start out at 38,000 then continue up with commission sales.
download the data here and run a pearson's correlation between gratitude and prosocial attitudes. use jasp. what is the null hypothesis of this study?
The null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.
What is the null hypothesis of the research?A study has been carried out to determine the relationship between gratitude and prosocial attitudes. JASP is used to run a Pearson correlation test between gratitude and prosocial attitudes. The null hypothesis of this study is that there is no correlation between gratitude and prosocial attitudes.
In this investigation, the Pearson correlation is used. This research aims to identify the relationship between gratitude and prosocial attitudes. It can be difficult to determine whether or not there is a correlation between two variables. Pearson's correlation is a statistical method that can be used to examine the correlation between two variables.
This research is carried out with the hypothesis that there is a relationship between gratitude and prosocial attitudes. In this study, the null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.
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What are the integer solutions to the inequality below?
3<3x−3≤2x+2
Hence, x = 4 is the only integer answer to the inequality as the range of possible values for x is from 4 to 5.
what is inequality ?A mathematical statement showing a connection that exists between values or statements that aren't always equal is known as an inequality. Inequalities compare two quantities using symbols like (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, "y -3" denotes that the y value is more than or equal to -3, whereas "x 5" denotes that the x value is less than 5. A number line can be used to depict all the possible numbers that satisfy an inequality after it has been solved. In many different mathematical fields, including the solution of equations, the study of functions, and the definition of relationships between variables, inequality is used.
given
We can begin by finding the inequality's x:
3 < 3x - 3 ≤ 2x + 2
To add 3 to each of the inequality's three components, we get:
6 < 3x ≤ 2x + 5
When we deduct 2x from each of the inequality's three components, we obtain:
4 < x ≤ 5
Since we are seeking for integer answers, the range of possible values for x is from 4 to 5, with 5 being the exception. Hence, x may be:
x = 4
Hence, x = 4 is the only integer answer to the inequality as the range of possible values for x is from 4 to 5.
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2. The given table provides four points along a line. What is the slope of the line in simplest form?
A. 1/2
B. -1/2
C. 2
D. -2
Therefore, the slope of the line passing through the given points is -1/2.
What is slope?In mathematics, the slope is a measure of the steepness of a line. It refers to the ratio of the vertical change to the horizontal change between any two points on the line. The slope of a line is often denoted by the letter "m."
For a given line, the slope is calculated by taking any two points on the line, [tex](y_{1} ,y_{2}[/tex] and [tex](x_{1} ,x_{2}[/tex] and applying the formula:
slope [tex]m= (y_{2} -y_{1})/(x_{2}-x_{1})[/tex]
The slope can be positive, negative, zero, or undefined, depending on the direction and steepness of the line. A positive slope means that the line is increasing as you move from left to right, while a negative slope means that the line is decreasing. A zero slope means that the line is horizontal, and an undefined slope means that the line is vertical.
by the question.
To find the slope of the line passing through the given points, we can use the slope formula:
slope = (change in y)/(change in x)
Let's choose the first point (-8, -21) and the last point (10, -30) to calculate the slope:
change in y = -30 - (-21) = -9
change in x = 10 - (-8) = 18
slope = (-9)/18 = -1/2
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The cost (in dollars)of a custom-made T-shirt is represented by 0. 75n + 9. 99, where n is the number of words in the design. Write and interpret a simplified expression that represent the cos5t of 12 T-shirt
The cost of 12 custom-made T-shirts with 12 words in the design is 149.88 dollars.
The cost for 12 custom-made T-shirts can be represented by the simplified expression 0.75n + 119.88, where n is the number of words in the design. For example, if the design has 12 words, the cost of the 12 T-shirts is 0.75*12 + 119.88 = 149.88 dollars. This expression means that for each T-shirt, there is an additional cost of 0.75 dollars for each word in the design, plus a flat fee of 9.99 dollars per T-shirt. This can be interpreted as the cost of each T-shirt increases with the complexity of the design.
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8x=-10y slope and y intercept
Answer:
To solve the equation 8x = -10y for the slope and y-intercept, we need to first rearrange it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can divide both sides of the equation by -10, which gives us:
y = (-8/10)x
Simplifying further, we get:
y = (-4/5)x
Therefore, the slope of the line represented by this equation is -4/5. This means that for every increase of 1 in x, y decreases by 4/5.
To find the y-intercept, we can set x to 0 and solve for y:
y = (-4/5)(0)
y = 0
Thus, the y-intercept is 0.
In summary, the slope of the line represented by 8x = -10y is -4/5 and its y-intercept is 0.
Step-by-step explanation:
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Answer: x=5y/4
Step-by-step explanation:
8x=10y
Divide both sides by 8
8x/8 = 10y/8
8x divided by 8, will cancel out resulting in x.
So, your final answer will be x=5y/4
An owl is flying 42 m above a field when it sees a mouse.
The distance from the owl to the mouse is 78 m.
Work out the angle of depression from the owl to the mouse.
Give your answer to 3 s.f.
Hence, there is a 28.22 degree depression from the owl to the mouse as the inverse tangent of the two sides.
what is angle ?An angle is a geometric shape made up of two rays or lines that share a termination known as the vertex. A whole circle has 360 degrees, which is how angles are typically measured. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (more than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), reflex, or compound (any combination of these) (greater than 180 degrees but less than 360 degrees). Calculus, geometry, trigonometry, and other branches of mathematics all make use of angles.
given
To resolve this issue, we can make use of the tangent function. Let x be the depression angle between the owl and the mouse. Next, we have:
Tangent(x) = adjacent/opposite
where the distance between the owl and the mouse is on the adjacent side and the opposite side is the height of the owl above the field (42 m) (78 m).
Tangent(x) equals 42/78
When we take the inverse tangent of the two sides, we obtain:
x = (42/78) arctan
Calculating the answer, we discover:
28.22 degrees x
Hence, there is a 28.22 degree depression from the owl to the mouse as the inverse tangent of the two sides.
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if one of the 1127 people is randomly selected, find the probability that the person is a man or a heavy smoker
The required probability of randomly selected person to be a man or a heavy smoker is given by 0.5525.
Total number of people is equals to 1124
Total number of men is equals to 531
Total number of heavy smoker is equals to 90
Man and Heavy smoker are mutually exclusive events.
Let 'M' represents man
And 'H' represents heavy smoker
Probability of randomly selected person is a man or a heavy smoker
= P( M ∪ H )
= Probability of a man + Probability of a heavy smoker
= P( M ) + P (H)
= ( 531 / 1124 ) + ( 90 / 1124 )
= ( 621 / 1124 )
= 0.5525
Therefore, the probability of a person to be a man or a heavy smoker is equals to 0.5525.
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The above question is incomplete, the complete question is:
If one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker.
table is attached.
in a one-sided hypothesis test for the mean for a random sample of size 20, the t-score of the sample mean is 2.615 in the direction of the alternative. is this significant at the 5% level? at the 1% level?
In a one-sided hypothesis test for the mean for a random sample of size 20, the t-score of the sample mean is 2.615 in the direction of the alternative. This significant at the 5% level and not significant at 1% level.
In hypothesis testing, the t-score measures how many standard errors the sample mean is from the hypothesized population mean. The formula for calculating the t-score is:
t = (sample mean - hypothesized population mean) / (standard error of the mean)
In this case, we are given that the t-score is 2.615 and that it is in the direction of the alternative hypothesis (which means the sample mean is greater than the hypothesized population mean). We can use a t-table or a statistical software to find the p-value associated with this t-score.
Assuming a two-tailed test (since we don't know if the alternative hypothesis is greater than or less than the null hypothesis), the p-value is the probability of getting a t-score greater than or equal to 2.615 or less than or equal to -2.615 (the negative value since it's a two-tailed test).
Using a t-table with 19 degrees of freedom (since the sample size is 20 and we are estimating one parameter), we find that the p-value is approximately 0.014 for a one-tailed test in the direction of the alternative.
To determine if the result is significant at the 5% level or 1% level, we compare the p-value to the significance level (alpha). If the p-value is less than alpha, we reject the null hypothesis and conclude that the result is statistically significant.
For a one-tailed test at the 5% level, alpha = 0.05. Since the p-value (0.014) is less than alpha, we reject the null hypothesis and conclude that the result is significant at the 5% level.
For a one-tailed test at the 1% level, alpha = 0.01. Since the p-value (0.014) is greater than alpha, we fail to reject the null hypothesis and conclude that the result is not significant at the 1% level.
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In how many ways can 8 distinguishable rooks be placed on an 8 × 8 chessboard so that none can capture any other, namely no row and no column contains more than one rook? For example, in a 2 × 2 chessboard, you can place 2 rooks labled 'a, and 'b' in 4 ways. There are 4 locations to place'a', and that location determines the location of b'.
There are 40,320 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.
In order to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other, we need to place one rook in each row and each column exactly once.
The first row can be filled in 8 ways, as there are 8 columns to choose from. The second row can be filled in 7 ways, as we cannot choose the column that has already been filled in the first row. Continuing in this way, we see that the number of ways to place 8 distinguishable rooks on an 8 × 8 chessboard is:
8! = 40,320
Therefore, there are 40,320 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.
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Number 12 please help me
On solving and factorizing the equation;
1). 2(3x+2y)
2.) 2(5x+4y)
3.) 3(2x+3y)
Define factorizationFactorization is the process of expressing a number or an algebraic expression as a product of its factors, which are numbers or expressions that multiply together to give the original number or expression. In other words, factorization involves breaking down a larger number or expression into smaller factors.
First expression12(4x+3y)-2x-2y
Solving the expression
8x+6y-2x-2y
6x+4y
Factorizing the expression , we get
2(3x+2y)
First expression22(4x+3y)+2(x+y)
Solving the expression
8x+6y+2x+2y
10x+8y
Factorizing the expression , we get
2(5x+4y)
First expression32(4x+4y)-2x+y
Solving the expression
8x+8y-2x+y
6x+9y
Factorizing the expression , we get
3(2x+3y)
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What is the square root of 16?
A submarine dives 240 meters below the surface of the water and then rises 65 meters.
Which integer describes the position of the submarine in relation to the surface of the
water?
A. -305 m
B. -175 m
C.175 m
D 305 m
Answer:
B
Step-by-step explanation:
-240 +65 = -175
(We use a -240 instead of 240 because it's below water.) :)
A cylindrical cooler is filled with juice. The container has a radius of 7 inches and a height of 18 inches. If a cubic inch contains about 0.004 gallons of juice, how many gallons of juice does the container hold?
V = πr^2h
V = π7^2•18
V = π49•18
V = 2770.88472
= 2770.88472 • 0.004
= 11.083538
Thus, the container holds 11.08 gallons of juice.
What is the volume of the composite solid? Use 3.14 for πr and round your answer to the nearest cm³.
A. 733 cm³
B. 707 cm³
C. 1099 cm³
D. 471 cm³
7 cm
Answer:179 cm3
there you go :)
Step-by-step explanation:
Find the volume of the prism shown below.
7 in.
12 in.
5 in.
Answer: 420 in ³
Step-by-step explanation:
The Formula for finding the volume of a prism = Length x Breadth x Height
Volume of prism = 7 x 5 x 12
= 420 in³
Math help question 1
How many sixth graders attend your school
(A statistical question)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
354?
Step-by-step explanation:
Thats my guess around 354 6th graders are there in my school
11. What uniform is never authorized as a "Uniform of the Day?" In njrotc
Answer:
The Summer Blue Uniform.
Step-by-step explanation:
NJROTC contains many different policies and guidelines for cadets.
a) Complete the number machine so that z = 5w-3 Input b) Write down the output y in terms of x. Input X +2 x 7 Output Z Output y
When x + 2 is plugged into the number machine, the output y is 5x + 7.
The number machine can be expressed mathematically as z = 5w - 3, where w is an input value and z is the output value. In this case, the input value is x + 2 and the output value is y.
To calculate y in terms of x, we can substitute x + 2 for w in the equation:
z = 5(x + 2) - 3
y = 5x + 10 - 3
y = 5x + 7
Therefore, when x + 2 is plugged into the number machine, the output y is 5x + 7.
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95.04 divided by 0.0132
[tex]x=95.04\div0.0132[/tex]
[tex]95.04\div0.0132=7,200[/tex]
[tex]\bold{x=7,200}[/tex]
Answer:
7200
Step-by-step explanation:
Use the numbers given divide, move the decimal place to the right of 0.0132 until you get 132.
Then divide 95.04 over 132
When 95.04/132=0.72
Then move the decimal four times because 0.0132 to 132 takes times 10000
So 0.72 move the decimal four times or times 10000 you will get 7200
Final answer 7200
the average late fee for 360 credit card holders was found to be $56.75. what variable would the 360 be?
The variable that 360 represents in this context is the sample size or the number of credit card holders in the sample.
The fact that the average late fee was calculated based on the data from 360 credit card holders implies that a sample of 360 credit card holders was selected from a larger population of credit card holders, and the average late fee was calculated from this sample.
The sample size is an important variable in statistics because it affects the accuracy and precision of the estimates we make based on the sample data. In general, larger samples tend to provide more reliable estimates of population parameters, such as the population mean or the population standard deviation.
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Can someone check this because its due tomorrow!
Answer:
Step-by-step explanation:
Subtract: 22²+8242²+122-16
O22²+122-12
4(x+4)(x-1)
O -x²+12x-12
4x(x+4)(x-1)
-2²+6x-6
о 22(x+4)(x-1)
H
-2x²+12-12
2(x+4)(x-1)
=
6-2(x-1)
6
2x(x+4)= 4(x+4)(x-1) = 2z(x+4)-2(x-1)
x.x
4(x+4)(x-1)-
Answer:
the correct answer is the second one
Step-by-step explanation:
I will add a photo of my solution, because there's a lot to type here
To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.
It is TRUE that If you want to calculate the total magnification, take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.
If you want to get the total magnification of a microscope, you need to multiply the magnification of the objective lens by the magnification of the eyepiece lens. The objective lens typically has a magnification of 4X, 10X, or 40X, and the eyepiece lens usually has a magnification of 10X. So, for example, if you are using a 10X objective lens and a 10X eyepiece lens, the total magnification would be 10 × 10 = 100X.
On the other hand, these numbers may be the total magnification for a lower powered stereomicroscope. 10X and 40X are achievable with 10X eyepieces and 1X or 4X objective lenses. Or it can be a zoom stereomicroscope with zoom set to 1X and 4X and 10X eyepieces. To get a total of 4X, you can use the 0.8X zoom setting (which is common) plus the 5X eyepiece. Or you can use the 0.5x auxiliary lens, 0.8x zoom and 10x eyepieces.
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Complete Question:
True, or False
To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.
the coefficient of determination measures the variation in the dependent variable that is explained by the regression model.T/F
The statement "the coefficient of determination measures the variation in the dependent variable that is explained by the regression model" is true because coefficient of determination, or R-squared, measures the proportion of variance in the dependent variable that is explained by the independent variables in a regression model.
The coefficient of determination, or R-squared, is a statistical measure that evaluates the goodness of fit of a regression model. It quantifies the amount of variance in the dependent variable that can be explained by the independent variables in the model. R-squared ranges from 0 to 1, where a value of 0 means that none of the variation in the dependent variable is explained by the model, while a value of 1 indicates that all the variation is explained.
Therefore, R-squared is useful in assessing the predictive power of a model, and higher values are generally preferred. However, it is important to note that R-squared alone does not guarantee a good model, and other factors such as model assumptions and outliers should also be considered.
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For 5-8, find the measure of each angle.
5. The angle turns through 1/5 of the circle.
A circle is a curve sketched out by a point moving in a plane. The measure of the angle is 72°.
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Let the angle that turns through 1/5 of the circle be x.
We know that the measure of the center of a circle is 360°, while it is given that the angle turns through 1/5 of the circle. Therefore, the angle will turn 1/5 of 360°.
x = 1/5 of 360 = 72°
Thus, the measure of the angle is 72°.
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