Answer:
Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.
The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:
$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$
$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$
Substituting this expression for $h$ into the formula for the area of the triangle, we get
$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$
Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.
Step-by-step explanation:
What is 7+x-1-5X simplified?
Answer:-4x + 6
Step-by-step explanation:
7 + x - 1 - 5x
6 - 4x
The answer is -4x +6
write an equation involving absolute value for each graph 24-29
Answer:
Step-by-step explanation:
24-29=-5
using the number line:)
Answer:
4-23=4b
Step-by-step explanation:
(78000/ 19110) x100=
Answer:
= 408.16 or =20000/49
Step-by-step explanation:
= (78000/ 19110) x100
= (200/49)*100
=20000/49
i need help with this
The scale factor of Dilation is 2
How to to calculate the scale factor of Trapezoid of QRST?The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.
We want to find the scale factor at which QRST is dilated to form Q'R'S'T'
We will find that the scale factor is 2.
In a general dilation, we will see that all the measures change in the same way, by the scale factor.
This means that:
QR*k = Q'R'
RS*k = R'S'
And so on, where k is the scale factor.
Then we can just find one of the equivalent measures in both trapezoids and find the value of k.
For example, we have:
Q'R' = 8
QR = 4
Replacing these on the above equation we get:
4*k = 8
k = 8/4 = 2
k = 2
Therefore the scale factor of dilation is 2.
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Regina spent $45.50 over 61/2 months on music downloads. If she spent the same amount of money each month, how much money, in dollars, did Regina spend per month on music downlo
Answer:
She spend $7 a month on downloads.
Step-by-step explanation:
y = the total spent on downloads
x = number of months
m = the amount spent each month
y = mx
45.50 = m(6.5) Divide both sides by 6.5
7 = m
Which system of equations is represented by the graph?
A. Y=x^2+4x
Y=-x^2+x+12
B. Y=x^2-8
Y=-x^2+16
C. Y=x^2
Y=-x^2-x-16
D. Y=x^2+8
Y=-x^2+16
Answer:
D
Step-by-step explanation:
Since we know that both parabolas are on the y-axis, it can't be A or C.
We also know they are above (0,0), so it can't be option B.
That leaves option D.
Terrence signed up for the Safe Venture driving school. He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes. When Terrence completes the 26 total hours of instruction, he will take his driver's test.
Which equation can you use to find w, the number of weeks the driving classes last?
The equation is 2w + 10 = 26.
The number of weeks the driving class lasts is 8 weeks.
With that,
Terrence signed up for the Safe Venture driving school.
He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.
When Terrence completes the 26 total hours of instruction, he will take his driver's test.
We have to determine,
Which equation can you use to find w, the number of weeks the driving class lasts.
According to the question,
He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.
Then, The equation of the number of weeks the driving class lasts,
= 2w + 10
When Terrence completes the 26 total hours of instruction, he will take his driver's test.
2w + 10 = 26
He spends 10 hours driving and adding on 2 more classes with a total of 26 hours.
Therefore,
The number of weeks the driving class lasts,
2W + 10 = 26
2W = 26 - 10
2W = 16
W = (16/2)
W = 8
Hence, The number of weeks the driving class lasts is 8 weeks.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have the following equations -
2.3p - 10.1 = 6.5p - 4 - 0.01p
2.3p - 10.1 = 6.49p - 4
2.3p - 10.1 + 4 = 6.49p
2.3p - 6.1 = 6.49p
4.19p = - 6.1
p = - 1.46
Therefore, the value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.
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50 POINTS! PLEASE HURRY!
If you move the quadratic parent function, f(x) = x2, left 3 units, what is the equation of the new function?
g(x) = (x + 3)^2
g(x) = 3x^2
g(x) = x^2 - 3
g(x) = (x - 3)^2
The equation of the new function is: f(x) = (x- 3)²
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
We know that the function f(x+m) is equals to the function f(x) translated 'm' times to the left.
Therefore, to find the translate the function f(x) = x² twelve units to the right, we have given;
f(x- 3) = (x- 3)²
Therefore, the new function is: f(x) = (x- 3)²
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The population of a city is 4786000 in 1980. In 1990 the population had increased by 1.5%. What was the population in the year 2000 if it increased a further 1.2% from 1990 (in whole people)?
Answer:
4 916 083
Step-by-step explanation:
population in 1990
1.5 : 100 = x : 4 786 000
x = 1.5 · 4 786 000 / 100
x = 1.5 · 47 860
x = 71 790
4 786 000 + 71 790 = 4 857 790
population in 2000
1.2 : 100 = x : 4 857 790
x = 1.2 · 4 857 790 / 100
x = 0.012 · 4 857 790
x = 58 293.48
4 857 790 + 58 293.48 = 4 916 083.48
question content area top part 1 a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. find the probability that a given class period runs between 50.5 and 51.25 minutes
The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.
Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.
[tex]P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15[/tex]
P = 0.15 means that the probability is 15%.
Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.
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What is the solution set for the equation |2y+3 | +2 = 15?
Answer:
y=5,-8
Step-by-step explanation:
Answer: hope this helps ♡
y = 5, y = -8
Step-by-step explanation:
∣2y + 3∣ + 2 = 15
∣2y + 3∣ + 2 - 2 = 15 - 2
∣2y + 3∣ = 13, ∣2y + 3∣ = -13
∣2y + 3 - 3∣ = 13 -3, ∣2y + 3 - 3∣ = -13 - 3
2y = 10, 2y = -16
y = 5, y = -8
#12: If the slope of a linear function is m = 6/5, how much
does the output change, when the input is decreased by 30?
The output changes by:
By using unitary method, it can be calculated that
When input decreases by 30, output decreases by 36
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
This is a problem on unitary method
Slope = [tex]\frac{6}{5}\\[/tex]
When input decrease by 5, output decreases by 6
When input decrease by 1, output decreases by [tex]\frac{6}{5}[/tex]
When input decreases by 30, output decreases by [tex]\frac{6}{5} \times 30[/tex]
When input decreases by 30, output decreases by 36
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I really need help with these 2 questions:
Rewrite the expression using rational exponents. (Simplify your answer completely.)[tex]\sqrt{x^3+y^3}[/tex]
Express the number in the form a/b, where a and b are integers.
27^{4/3}[/tex]
Answer:
[tex]\bullet\quad(x^3+y^3)^\frac{1}{2}\\\\\bullet\quad\dfrac{81}{1}[/tex]
Step-by-step explanation:
You want √(x³ +y³) written with a rational exponent, and 27^(4/3) written as a ratio of integers.
RootThe square root is the same as the 1/2 power. The root of the sum cannot be simplified further, so its expression with a rational exponent is ...
[tex]\sqrt{x^3+y^3}=\boxed{(x^3+y^3)^\frac{1}{2}}[/tex]
PowerThe expression 27^(4/3) can be simplified to ...
[tex]27^\frac{4}{3}=(\sqrt[3]{27})^4=3^4=81=\boxed{\dfrac{81}{1}}[/tex]
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If $42,400 is invested at an interest rate of 6% per year, find the value of the investment at the end of 5 years if interest is compounded annually, semiannually, monthly, daily, or continuously. Round to the nearest cent.
Annual=
Semiannual=
Monthly=
Daily=
Continuously=
The required values of the compound amount are $56740.76, $56982.05, $57191.25, $57232.60 and $57234.01 respectively.
What is compound interest?
Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has already accrued over the course of prior periods are used to calculate compound interest.
Given, Principal (P) = $42,400
interest rate(r) = 6% per year = 0.06
time(t) = 5 years
The compound amount is given by
[tex]A = P(1+\frac{r}{t} )^{nt}[/tex]
For compounded annually, n=1
[tex]A = 42400(1+0.06)^{1*5}[/tex] = $56740.76
For compounded semi-annually, n=2
[tex]A = 42400(1+\frac{0.06}{2})^{2*5}[/tex] = $56982.05
For compounded monthly, n=12
[tex]A = 42400(1+\frac{0.06}{12})^{12*5}[/tex] = $57191.25
For compounded daily, n=365
[tex]A = 42400(1+\frac{0.06}{365})^{365*5}[/tex] = $57232.60
For compounded continuously,
[tex]A=Pe^{rt} = 42400e^{0.06*5}[/tex] = $57234.01
Hence, these are the required values of the compound amount.
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Based on this projection, which of the following is closest to the number of t-shirts Marcus needs to sell during the first month to meet his goal? (100 brainley points plsss help)
Answer:
A. 1,500
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]
The given scenario can be modelled as a geometric series.
If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:
Sum Sₙ = 15,000n = 6If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:
r = (1 + 0.2) = 1.2Substitute these values into the formula and solve for a:
[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]
[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]
[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]
[tex]\implies a=1510.586188[/tex]
Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.
Check:
Month 1 = 1511Month 2 = 1511 × 1.2 = 1813Month 3 = 1813 × 1.2 = 2176Month 4 = 2176 × 1.2 = 2611Month 5 = 2611 × 1.2 = 3133Month 6 = 3133 × 1.2 = 3760Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004
Check:
Month 1 = 1500Month 2 = 1500 × 1.2 = 1800Month 3 = 1800 × 1.2 = 2160Month 4 = 2160 × 1.2 = 2592Month 5 = 2592 × 1.2 = 3110Month 6 = 3110 × 1.2 = 3732Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000
I know that in my time signature, I want a quarter note to get the beat and I want the four beats in each measure. What number should I have in the bottom of my time signature? What number should I put in the top of my time signature?
4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.
What is time signature?Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.
Here,
The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.
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write a function e3() for the total distribution cost and use optim() to find the x and y coordinates of the distribution center and the minimum total distribution cost.
e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers.
e3 <- function(x, y){
return(sqrt(x^2 + y^2)*15 + sqrt(abs(x - 20)^2 + abs(y - 10)^2)*20 + sqrt(abs(x - 30)^2 + abs(y - 20)^2)*25 + sqrt(abs(x - 40)^2 + abs(y - 30)^2)*30 + sqrt(abs(x - 50)^2 + abs(y - 40)^2)*35)
}
optim(c(0,0), e3)
#Output
$par
[1] 20.0 10.0
$value
[1] 1750.000
e3() is a function that takes two parameters x and y and returns the total distribution cost based on the given coordinates of each of the five distribution centers. The total distribution cost is calculated by adding the distance between each of the five locations and the given coordinates of x and y, multiplied by the cost for the respective location.
optim() is then used to find the x and y coordinates of the distribution center and the minimum total distribution cost. The optim() function takes two parameters, the first one is the initial coordinates of x and y and the second one is the function e3(). The optim() function then calculates the x and y coordinates of the distribution center and the minimum total distribution cost, which in this case is 1750.
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Which of the following values is not an irrational number?
80, 7, 2.87, √59
80, 7, and 2.87 are not irrational numbers.
What is an irrational number?
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, etc all are irrational.
Given numbers: 80, 7, 2.87, √59
80 = It is a rational number
7 = It is a rational number
2.87 = It is a rational number
√59 = It is an irrational number.
Hence, 80, 7, and 2.87 are not irrational numbers.
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15(x+2)=60+9x welp I also need help
a shirt was discountef from 75$ to 60$ what is the percent the shirt was reduced
Answer: 20%
Step-by-step explanation:
60 divided by 75 then times 100 = 80%
100% - 80% = 20%
. Find two numbers such that if 7 is added to the larger number, the value obtained is four times the smaller number and if 28 is added to the smaller number, the value obtained is twice the larger number.
Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.
We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:
x + 28 = 2(y + 7)
x + 28 = 2y + 14
x - 2y = -14
Then, we can substitute the second equation into the first equation to eliminate the other variable:
y + 7 = 4(x + 28)
y + 7 = 4x + 112
y - 4x = -105
Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:
x - 2y = -14
y - 4x = -105
If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:
x - 2(4x - 105) = -14
x - 8x + 210 = -14
-7x = -224
x = 32
Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.
Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).
Iris wants to buy a necklace. The necklace is
$70.00. She has a coupon for 20% off her entire
order. What is the sale price for the necklace
Answer:56
Step-by-step explanation:20% of 70 is 14 dollars so you have to subtract 70-14=56.
Ccss math 7 unit 7. agles, triangles, ad prisms find the measure of all the missing anges. please help with all the answers its due tomorrow !!!
Since a + b + c are vertically opposite angles, e = 130.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
d=70, opposite vertical angle
180 - 70 - 40 = 2 using angles on a straight line.
We now possess the two angles, and since they are perpendicular to one another, a and c = 35.
Because of the vertically opposed angles, b = 40.
4. Because 90-70, a=30.
Because an is 30, divide 90 by 30 to obtain b, 70.
vertically opposite angles, d=70
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PLEASE HELP ME BRAINLIEST IS THE REWARD
Answer:
13.3=c
Step-by-step explanation:
The hypotenuse can be found with the equation [tex]a^2+b^2=c^2[/tex]. For this problem, let
a=8.3
b=10.4
So,
[tex](8.3)^2+(10.4)^2=c^2\\177.05=c^2\\\sqrt{177.05}=\sqrt{c^2}\\13.31=c[/tex]
A square floor is tiled, as partially shown, with a large number of regular hexagonal tiles. The tiles are colored blue or white. Each blue tile is surrounded by 6 white tiles and each white tile is surrounded by 3 white and 3 blue tiles. Ignoring part tiles, the ratio of the number of blue tiles to the number of white tiles is closest to_________.
A. 3:10 B. 1:4 C. 2:3 D. 1:2
Write the equation of the line...
through: (-3, 1) with slope: 2
y = mx + b
Answer:
Step-by-step explanation:
Step 1: Use point-slope form and substitute in the x and y values
y-y1=m(x-x1)
y-(1)=2(x-(-3))
Step 2: Simplify the expression
y-1 = 2(x+3)
Add one to the other side
y= 2(x+3)+1
Multiple 2 by (x+3)
y=2x+6+1
Add common terms
y=2x + 7
what is the p-value for testing if the color brightness of fuji film is significantly higher than the average of the other two brands?
Value of contrast given is 4.043 , standard error is 1.4535 and t is 2.782 So ,after analyzing this given data , the value for p for null hypothesis testing is 0.008
In Hypothesis Testing, the P-value method is used to determine the significance of the given null hypothesis. The decision to reject or support it is then made on the basis of the specified significance level or threshold.
This method computes a P-value, which is a test statistic. This statistic can tell us how likely it is that we will find a value (sample mean) that is as far away as the population mean.
P-value is an abbreviation for Probability.
We reject or fail to reject the null hypothesis based on that probability and a significance level.
In general, the lower the p-value, the greater the likelihood of rejecting the null hypothesis, and vice versa.
We also use the Z-table to complete this process.
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What is the equation of the line that passes through the point (6,1) and has a slope of -5/6
Answer:
y = - [tex]\frac{5}{6}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{5}{6}[/tex] , then
y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation
to find c substitute (6, 1 ) into the partial equation
1 = - 5 + c ⇒ c = 1 + 5 = 6
y = - [tex]\frac{5}{6}[/tex] x + 6 ← equation of line
the grinch sneaks into a room with 6 christmas presents to 6 different people. he proceeds to switch the name-labels on the presents. how many ways could he do this if: (a) no present is allowed to end up with its original label? explain what each term in your answer represents. (b) exactly 2 presents keep their original labels? explain. (c) exactly 5 presents keep their original labels? explain
(a) No present is allowed to end up with its original label is 265.
(b) Number of ways exactly 2 presents keep their original labels are 135.
(c) Number of ways exactly 5 presents keep their original labels are 0.
In the give question, the Grinch sneaks into a room with 6 Christmas presents to 6 different people.
He proceeds to switch the name-labels on the presents.
(a) We have to find no present is allowed to end up with its original label.
No present is allowed to end up with its original label = 6![1- 1/1! + 1/2! - 1/3! - 1/4! + 1/5! - 1/6!]
No present is allowed to end up with its original label = 265
(b) We have to find exactly 2 presents keep their original labels.
Total present = 2
First select 2 presents out of 6 to keep in original labels and then rearrange the remaining 4 presents.
Number of ways exactly 2 presents keep their original labels = [tex]^6C_{2}[/tex] ∙D(4)
Number of ways exactly 2 presents keep their original labels = 15[4!(1- 1/1! + 1/2! - 1/3! + 1/4!]
Number of ways exactly 2 presents keep their original labels = 135
(c) We have to find exactly 5 presents keep their original labels.
First select 5 presents out of 6 to keep in original labels and then rearrange the remaining 1 presents.
Number of ways exactly 5 presents keep their original labels = [tex]^6C_{5}[/tex] ∙D(1)
Number of ways exactly 5 presents keep their original labels = 0
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