Option C, 59° is correct answer, The angle JIL is equal to 59 degree.
What is angle?
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.
Given information in the question,
∠HIL = (6x-7)°
∠JIL = (5x+4)°
The ray IL bisects the ∠HIJ
Since, IL bisects angle HIJ then, angle HIL = angle JIL
So,
6x - 7 = 5x + 4
x = 11
Putting the value of x in given value of JIL to get the angle JIL
∠JIL = (6x-7)°
∠JIL = (6(11)-7)°
∠JIL = 59°
Therefore angle JIL is equal to 59 degrees.
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the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. 1. what proportion of these banks had an interest rate less than 2.5 percent?
The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 2.5
μ = mean = 2.28
σ = standard deviation = 0.37
z-score = (2.5 - 2.28) / 0.37
z-score = 0.22 / 0.37
z-score = 0.5946
To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0.5946
By interpolating the values,
probability = 0.724
proportion = 0.724
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according to a survey of advanced curriculum high school students, the mean time spent studying each day is 6.4 hours. assume the standard deviation is 0.80 hours and that the probability distribution is normal. what is the 80th percentile for number of hours spent studying each day? round your answer to 2 digits after the decimal.
The 80th percentile for the number of hours spent studying each day is 7.07 hours.
A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.
The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.
Given Data :
Mean time (u) = 6.4 hour
Standard Deviation = 0.80 hour
It is given that the probability distribution is normal.
The formula for the z-score is z =( x- mean)/standard deviation
For the 80th percentile, the z value from the z table is 0.842.
We have,
0.842 = (x - 6.4)/0.8
0.842*0.8 = x - 6.4
0.6736 =x - 6.4
x = 0.6736 + 6.4
x = 7.0736
x = 7.07
Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.
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The line perpendicular to y=1/2x-2 that passes through the point (0,3)
⇒For perpendicular lines when their gradients are multiplied they have to give -1, in this case we are given a line with gradient [tex]\frac{1}{2}[/tex] meaning the gradient of the line perpendicular to it will be -2 since
[tex]-2*\frac{1}{2} =-1[/tex] this means that the gradient of the new line will be -2
⇒Now we have a point and gradient.
⇒And we know that the general equation for a straight line is y=mx+c
[tex]3=-2(0)+c\\3=c\\c=3[/tex]
The equation of the line perpendicular to the given one is
y=-2x+3
GOODLUCK!!
3What is the inverse of the function h(x) = - 2 + 12?h-'(x) =(2
We have the next function
[tex]h(x)=\frac{3}{4}x+12[/tex]First we need to make h(x)=y
[tex]y=\frac{3}{4}x+12[/tex]Then we make x=y and y=x
[tex]x=\frac{3}{4}y+12[/tex]Then we isolate the y
[tex]x-12=\frac{3}{4}y[/tex][tex]4(x-12)=3y[/tex][tex]y=\frac{4(x-12)}{3}[/tex][tex]y=\frac{4x-48}{3}[/tex]Therefore the inverse function is
[tex]h^{-1}(x)=\frac{4x-48}{3}[/tex]Find the volume of this object.Use 3 for π.Volume of a CylinderV= πr²h4 ft9 ft5 ft5 ft5 ftVolume of aRectangular PrismV = whV ≈ [?]ft³Enter
Mathematics → Solid Figures → Volume
The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]In this question,
r = 2 ft (4/2 =2)
h = 5 ft
Then, the volume of the cylinder is (Vc):
[tex]\begin{gathered} Vc=\pi *2^2*5 \\ Vc=\pi *4*5 \\ Vc=20\pi \end{gathered}[/tex]Using π = 3:
[tex]\begin{gathered} Vc=3*20 \\ Vc=60ft^3 \end{gathered}[/tex]The volume of a rectangular prism (Vr) is:
[tex]Vr=lwh[/tex]In this question:
l = 9 ft
w = 5 ft
h = 5 ft
Then, the volume of the rectangular prism is:
[tex]\begin{gathered} V=9*5*5 \\ V=225ft^3 \end{gathered}[/tex]The volume of the object (V) is the sum of the volumes:
[tex]\begin{gathered} V=Vc+Vr \\ V=60+225 \\ V=285ft^3 \end{gathered}[/tex]Answer: 285 ft³.
are 60/55 and 7/42 porportinal
y+1=3/2(x-1) in slope intercept form
Answer:
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
To get slope intercept form (y=mx+b), simplify and solve for y.
y+1=[tex]\frac{3}{2}[/tex](x-1)
Simplify
y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
Solve for y
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
-20 less than or equal to 4x
We will have the following:
[tex]-20\le4x[/tex]When we solve for x we will have
[tex]-\frac{20}{4}\le x\Rightarrow-5\le x[/tex]So, x is equal or grater than -5.
Sandra purchased $1,200 worth of electronic equipment on her new credit card, with an annual interest rate of 14.99%. If she has no other charges on the card and does not pay off the balance at the end of the month, how much money will she owe the credit card company after 1 month? Estimate the interest using the monthly periodic rate.
Given data:
The given amount of equipment purchased by the Sandra is A=$1,200.
Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches. What is the length of the pegboard?
The length of the rectangular pegboard is 80 inches
What is a rectangle?A rectangle is a polygon with four sides in which two opposite sides are parallel and equal
How to find the length of the rectangular pegboard?Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.
Let
L = length of pegboard and W = width of pegboard.Since the width of the pegboard is 8 inches less than half the length, we have that
W = L/2 - 8
Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)
Now, its perimeter P = 224 inches.
So, 2(L + W) = 224
L + W = 112
Now, substituting the width, W into the equation, we have
L + W = 112
L + L/2 - 8 = 112
L + L/2 = 112 + 8
L + L/2 = 120
3L/2 = 120
L = 120 × 2/3
L = 240/3
L = 80 inches
So, the length of the pegboard is 80 inches
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andrea wants to cut a board into three pieces the board is 3 2/3 feet long how long will each piece be
Answer:
7/6 feet
Step-by-step explanation:
The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.
3 + 1/2 = ?
3/1 + 1/2 = ?
6/2 + 1/2 = ?
(6 + 1)/2 = ?
= 7/2
3 + 1/2 = 7/2
In other words, the board is 7/2 feet long.
Now we have to divide by 3 since Andrea is cutting the board in three pieces.
So:
(7/2)/3 or (7/2) ÷ 3 or [tex]\frac{\frac{7}{2}}{3}[/tex] or (7/2) × (1/3)
= 7/(2×3)
= 7/6
So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.
Ms. lange drove about 150kms east from la sarre, to senneterre, quebec. she drove another 75kms north to lebel-sur-quevillon, what is the approximate air distance from la sarre to lebel-sur-quevillon
The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.
To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.
When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)
Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.
c² = a² + b²
where a = 150 km and b = 75 km
distance² = 150² + 75²
distance² = 22500 + 5625
distance² = 28125
distance = 167.71 km
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the mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5000. the distribution of incomes is skewed to the right. suppose that we select samples of size 43. determine whether the sampling distribution for is normal (or approximately normal) and give its mean and standard deviation.
The sampling distribution for is normal (or approximately normal) and give its mean and standard deviation is the mean is $28520 and its standard deviation is $762.5.
The notion of mean is crucial in both mathematics and statistics. The mean is the average or most frequent value among a set of numbers. It is a statistical measure used to determine the median and mode of a probability distribution's central tendency. It's also known as an expected value. Sum of all observations divided by the total observations equals the mean. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Given information :
Mean annual income = $28540
Standard Deviation = $5000
Given sample size is n = 43
Sample size doesn't affect the mean, hence the mean remains the same
New mean = $28540
New standard Deviation = Standard Deviation / n^1/2 = 5000/ (43)^1/2
New standard Deviation = 5000/6.5574 = $762.5
Hence, The mean is $28520 and its standard deviation is $762.5
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You will have $ in ten years if you set aside $500 a year at 10%.
Compound interest: $8,765.58
question
A group of friends’ dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill, including tax and tip, rounded to the nearest cent?
Responses
The cost of the total bill for the friends is $154.665.
What is a tax?This implies a levy that's paid to the government by individuals and firms.
From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.
The total bill will be:
= Cost of food + Tax + Tip
= $122.75 + (8% × $122.75) + (18% × $122.75)
= $122.75 + $9.82 + $22.095
= $154.665
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What is the solution to the inequality? 3(x+5)>12
Answer:
x>-2
Step-by-step explanation:
3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.
If p and q are integers and pq +p is an odd number, which of the following numbers must be even?
1-p
2-q
3- pq-3
4- p^2
Answer:Answer: number 2 is correct
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP
True or False: The set of whole numbers is closed under multiplication.
Explanation:
Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.
Examples:
2*3 = 65*7 = 3511*12 = 132In other words,
(whole number)*(whole number) = whole number
This is why we consider the set closed under multiplication.
How many times larger is (1.76 x 10^1) than (8 x 10^-1)
Answer:
14.7 times bigger is (1.176 x 10¹) than (8 × 10-¹) if the numbers are (1.176 x 10¹) than (8 × 10-¹).
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
To compare numbers this way, we divide.
(1.76 × 10^1) / (8 × 10^-1) =
= 1.76/8 × 10^1 / 10^-1
= 0.22 × 10^(1 - (-1))
= 0.22 × 10^2
= 22
given angle 1 is congruent toangle 3 and angle 12 is congruent to angle 8 prove l is parallel to m
Given that;
[tex]\angle1\cong\angle3,\angle12\cong\angle8[/tex]Line a and b are two straight lines cut by two transversal lines l and m.
The tranversal line l shows that;
[tex]\begin{gathered} \angle8\cong\angle6 \\ \end{gathered}[/tex]But also;
[tex]\angle8\cong\angle12[/tex]Thus,
[tex]\angle6\cong\angle12[/tex]Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Thus, line l is parallel to m
WILL GIVE BRAINLIEST find center, vertices, and foci of the ellipse.
cooling towers are used to remove or expel heat from a process. a cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. what is the width of the cooling tower at the base of the structure? round your answer to the nearest whole number. 100 meters 50 meters 48 meters 40 meters
The width of the cooling tower at the base of the structure is (D) 40 meters.
Where are cooling towers located?Typically, cooling towers are found on rooftops or other outdoor locations. Lower cooling system efficiency occurs as a result of operation and maintenance specialists commonly ignoring them because they are typically out of sight.Now, calculate the cooling tower's width:
Equation: x2/400 given (y-90)
²/1600=1Calculating the width:
Width of the cooling tower: 2400Width of cooling tower = 22040-meter cooling tower widthTherefore, the width of the cooling tower at the base of the structure is (D) 40 meters.
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passes through (1,4) and perpendicular to y=2x-7
The equation of the line is found as y = -x/2 + 9/2.
What is meant by the equation of the line?This is an x and y equation for whom solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b. In effect, x is used as a parameter, and y is written as just a function of x: y = f(x) = mx+b.For the given question;
The equation of the perpendicular line is given as;
y = 2x - 7
Compare the equation with the standard form of slope intercept.
y = mx + c
m = slope and c is the y intercept.
m1 = 2
Now, the line is perpendicular, thus the relation between both slopes is;
m1 × m2 = -1
m2 = -1/2
The passing coordinates of the line is (1. 4).
Find the equation using formula.
y - y1 = m2(x - x1)
y - 4 = (-1/2) (x - 1)
Simplifying,
y = -x/2 + 9/2
Thus, the equation of the line is found as y = -x/2 + 9/2.
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How do you solve this problem?
The area of the figure given below is 56.6 units² .
In the question ,
a figure is given
where there is one rectangle and two semicircles .
the length of the rectangle is given as 11 units
and the breadth of the rectangle is = 4 units
we know that the area of the rectangle is = length × breadth
on substituting the values ,
we get
area = 11 × 4
area = 44 units²
the radius of the semicircle = 2 units
the are of the semi circle = (1/2)*π*r²
since there are two semicircle , the area of the two semi circle will be
= 2 * (1/2)πr²
= π*r²
On substituting , the value of radius = 2 ,
we get the area is = 3.14*(2)² = 12.56 using π = 3.14
so the area of the complex figure is = 44 + 12.56 = 56.56
≈ 56.6
Therefore , The area of the figure given below is 56.6 units² .
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What is the answer for the equation:
7x+31 = 8x -1/3(27x+3) ?
The answer for the equation:
7x+31 = 8x -1/3(27x+3) is x=-4
. Represent Real World Problems Lorena and Benita are saving
money. They began on the same day. Lorena started with $40. Each
week she adds $8. The graph describes Benita's savings plan. Which
girl will have more money in 6 weeks? How much more will she
have? Explain your reasoning.
We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.
We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.
amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88
Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.
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15 points to help me out.
Answer:
can't answer the first two questions as figure is not mentioned in picture
3. -3
4. 6
5. 3/4
6. -3
7. 5
8. 3
Step-by-step explanation:
the distribution of the number of text messages young adults send per day is approximately normal, with a mean of 128 messages and a standard deviation of 30 messages. based on the distribution, what is the percentage of young adults send fewer than 218 text messages?
The percentage of young adults who send fewer than 218 text messages is 99.87%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 218
μ = mean = 128
σ = standard deviation = 30
z-score = (218 - 128) / 30
z-score = 90 / 30
z-score = 3
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 3
probability = 0.9987
To get the percentage, multiply the probability by 100.
percentage = probability x 100
percentage = 0.9987 x 100
percentage = 99.87%
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[tex]x + 49 \ \textgreater \ 28[/tex]I need it now please
To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.
So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:
[tex]\begin{gathered} x+49-49>28-49 \\ x>-21 \end{gathered}[/tex]The result of the inequality is x > -21