Answer:
$142500
Step-by-step explanation:
We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.
If the sum of the two salaries is $190000, we are to find the salary of the president of the University.
Let [tex]x[/tex] to be the department head's salary, we can write an equation:
[tex]3x+x=190000[/tex]
[tex]4x=190000[/tex]
[tex]x=47500[/tex]
Salary of the president of the University = [tex]3(47500)[/tex] = $142500
Answer:
$142,500
Step-by-step explanation:
Let's say x is the salary of the department head.... so the salary of the president of the university can be described as 3x.
Then, we know the total of the two salaries is 190,000. We can express this as:
3x + x = 190,000
4x = 190,000
x = 47,500
x is for the department head. To get the president's salary, we have to multiply that by 3:
p = 3 (47,500) = 142,500
The salary of the president is then of $142,500.
What is 2.5% of 89? Please tell me how to do this problem I am very confused
Answer:
2.225
Step-by-step explanation:
to get your answer you would multiply .025 by 89
Please give brainliest!!!
Answer:
2.225
Step-by-step explanation:
2.5% converted to a decimal is 0.025
2.5% of 89 really means 2.5%*89 because in math, of means multiply.
89*0.025=2.225
You have to multiply by the decimal because the percent is a proportion in reality.
Think about it this way:
Since 2.5% of 89 is 2.225, 97.5% of 89 has to be 89-2.225, which is 86.775
and it is:
89*0.975=86.775
This is because the percentage is equal to 1 in whole.
0.025+0.975=1 or 2.5%+96.5%=100%
use euler's formula to find the missing number vertices:16 edges:43 faces:?
Answer:
The number of faces is 29
Step-by-step explanation:
we know that
The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two
[tex]V- E + F= 2[/tex]
we have
[tex]V=16[/tex]
[tex]E=43[/tex]
substitute and solve for F
[tex]16- 43 + F= 2[/tex]
[tex]-27+F= 2[/tex]
[tex]F= 2+27[/tex]
[tex]F= 29[/tex]
2 raise to -3 can be written as _____________
Answer:
Step-by-step explanation:
2^(-3) = 1/2^3 = 1/8
A minus means put the number in the numerator if it was in the denominator.
A minus means put the number in the denominator it was in the numerator.
If there is no denominator, create one.
10. What is the mean of the data?
186, 181, 176, 149, 184, 190, 158, 139, 175, 111
Use synthetic substitution to find g(4) and g(–5) for the function g(x) = 3x4 – 5x2 + 7x – 7.
Answer:
Step-by-step explanation:
We write only the coefficients of the given equation inside the upside down symbol of division.
We first do synthetic substitution and then verify the result by putting g(4) and g(-5) in the original equation. Both should have the same result.
The questions are solved on the image attached.
Answer:
709, 1,708
Step-by-step explanation:
PLEASE HELP!! BRAINLIEST OFFERED! IF CORRECT!! THANKS!!
Answer:
Step-by-step explanation: its b
First, you'd have to decompose the shape. The way I decomposed it was by splitting the shape into a small rectangle and a large one. The formula for the rectangles is 6 times 3 and 6 by 9. You multiply 6 by 3 and get 18; then you multiply 6 by 9 and get 54. Lastly, you simply add 18 and 54. This gives you an answer; 72.
I WILL MARK BRAINLIEST
Answer:
24, 27, 30 (pattern is add 3)77, 92, 107 (pattern is add 15)12, 6, 3 (pattern is divide 2)Which expression is equivalent to (x^-4y/x^-9y^5)^-2
Answer:
[tex]\large\boxed{x^{-10}y^8=\dfrac{y^8}{x^{10}}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=(x^5y^{-4})^{-2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=(x^5)^{-2}(y^{-4})^{-2}=x^{(5)(-2)}y^{(-4)(-2)}=x^{-10}y^8\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{y^8}{x^{10}}[/tex]
A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, the wheel placement (center) and radius are modeled by the equation (x+2)^2+(y-0.5)^2=16. Which graph shows the position and radius of the wheels?
Answer:
The answer is the attached figure
Step-by-step explanation:
* Lets revise the equation of the circle
- The center-radius form of the circle equation is
(x – h)² + (y – k)2 = r², where the center is the point (h, k)
and the radius is r.
- This form of the equation is helpful, since you can easily find the
center and the radius.
* Now lets solve the problem
- The equation of the circle is (x + 2)² + (y - 0.5)² = 16
* Lets compare it with form above
∵ (x - h)² = (x + 2)²
∴ -h = 2 ⇒ × -1
∴ h = -2
∵ (y - k)² = (y - 0.5)²
∴ -k = -0.5 ⇒ × -1
∴ k = 0.5
∴ The center of the circle is (-2 , 0.5)
∵ r² = 16 ⇒ take √ for both sides
∴ r = √16 = 4
∴ The radius of the circle is 4 units
* Now lets look to the answer to find the circle whose center is
(-2 , 0.5) and radius 4 units
∴ The answer is the attached figure
* From the graph:
- The center of the circle is (-2 , 0.5)
- The horizontal diameter is between -6 and 2, then the length
of the diameter = 2 - -6 = 8
∵ The radius = 1/2 the diameter
∴ The raduis = 1/2 × 8 = 4 units
A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function: f(t) = −16t2 + 44t + 12 Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
Answer:
Reasonable domain is [1.375,3].
Step-by-step explanation:
Given function is [tex]f\left(t\right)=-16t^2+44t+12[/tex].
Now we need to find about what is the reasonable domain of the graph of the function [tex]f\left(t\right)=-16t^2+44t+12[/tex] when the basketball falls from its maximum height to the ground.
Compare with [tex]at^2+bt+c[/tex], we get a=-16 and b=44
then t-coordinate of vertex [tex]t=-\frac{b}{2a}=-\frac{44}{2\left(-16\right)}=1.375[/tex]
Then that means maximum height of the ball occurs when time t=1.375 seconds.
Now let's find time when ball falls on ground so set f(t)=0
[tex]f\left(t\right)=-16t^2+44t+12[/tex]
[tex]-16t^2+44t+12=0[/tex]
[tex]4t^2-11t-3=0[/tex]
[tex]\left(4t+1\right)\left(t-3\right)=0[/tex]
[tex]4t+1=0[/tex] or [tex]t-3=0[/tex]
[tex]4t=-1[/tex] or [tex]t=3[/tex]
[tex]t=-0.25[/tex] or [tex]t=3[/tex]
Time can't be negative so we use t=3 only
Hence reasonable domain is [1.375,3].
A point located at (-5, -6) is reflected over the y-axis. What are the coordinates of the image? (-5, 6) (5, -6) (5, 6) (-6, -5)
ANSWER
The image is located at (5,-6)
EXPLANATION
The rule for reflection over the y-axis is to negate the x-coordinates.
This implies that,
[tex](x,y)\to (-x,y)[/tex]
If the point located at (-5, -6) is reflected over the y-axis, the coordinates of the image is obtained by negating the x-coordinate.
Therefore
[tex]( - 5, - 6)\to (5, - 6)[/tex]
The image is located at (5,-6)
Answer:
The correct answer option is (5, -6).
Step-by-step explanation:
We are given the following coordinates of a point:
[tex] ( - 5 , - 6 ) [/tex]
If this point is reflected through y axis, what will be the coordinates of its image?
Reflection through y-axis means that the sign of the x coordinate will be changed so we get:
[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)
Do I multiply, please help
Answer:
yes
Step-by-step explanation:
to find the surface area, you need to find the area of all 6 sides using the dimensions given. each visible side has an opposite side that has the same dimensions.
1) 6*2=12
2) 6*2=12
3) 9*2=18
4) 9*2=18
5) 9*6=54
6) 9*6=54
then, you have to add all 6 sides together.
12+12+18+18+54+54
24+36+108
60+108
168 cm squared is the surface area
which event has a probability closest to 1? Choosing a boy randomly in a class of 10 boys and 10 girls, drawing a heart randomly out of a pile of 4 hearts and 8 spades, correctly choosing a random number between 1 and 10, choosing a girl randomly in a class of 8 girls and 12 boys
Answer:
Choosing a boy randomly in a class of 10 boys and 10 girls
Step-by-step explanation:
The probability of choosing a boy randomly in a class of 10 boys and 10 girls is calculated as;
(number of boys)/ (total number of students in the class)
= 10/(10+10) = 10/20 = 1/2
The probability of drawing a heart randomly out of a pile of 4 hearts and 8 spades is calculated as;
4/(4+8) = 4/12 = 1/3
The probability of correctly choosing a random number between 1 and 10 is simply 1/10 since the numbers are have a uniform distribution and thus equally likely to be selected.
The probability of choosing a girl randomly in a class of 8 girls and 12 boys is calculated as;
(number of girls)/ (total number of students in the class)
= 8/20 = 2/5
Thus choosing a boy randomly in a class of 10 boys and 10 girls is the event which has a probability closest to 1.
Final answer:
Out of the given events, choosing a boy randomly in a class of 10 boys and 10 girls has the highest probability, which is 0.5. Therefore, this event's probability is closest to 1.
Explanation:
To answer which event has a probability closest to 1, we need to calculate the probability of each event:
Choosing a girl randomly in a class of 8 girls and 12 boys has a probability of
8 girls / (8 girls + 12 boys) = 8/20 = 2/5 or 0.4.
Comparing these probabilities, choosing a boy randomly in a class of 10 boys and 10 girls has the highest probability, which is 0.5. Therefore, this event has a probability closest to 1.
In playing from the tee, a golfer hooks his drive (hits the ball to the left of the correct direction) at an angle of 24 from the intended direction. He estimates that he has driven the ball 215 yards and that it lies 100 yards from the hole. Assuming his estimates are correct, what is the distance from the tee to the hole, to the nearest yard?
Answer:
245 yards
Step-by-step explanation:
Answer:
245 yards
Step-by-step explanation:
You could say the tee is at (0, 0) and the hole lies on the x-axis.
The path of the ball is the straight-line so, y = tan(24°)x
215cos(24°) = 196.4
215sin(24°) = 87.4
The ball lands at coordinates (196.4, 87.4).
They say the ball lands 100 yards from the hole, the hole is on a circle of radius 100 that is centered at (196.4, 87.4).
Equation of the circle:
(x-196.4)² + (y-87.4)² = 100²
Since the hole is on the x-axis, it lies at the intersection of the circle and the line y = 0 so:
(x - 196.4)² + (0 - 87.4)² = 100²
x = 244.92
The distance between tee and hole is 245 yards.
what does it mean by “what is the unit rate?” what is a unit rate?
Answer:
A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Common examples of "unit rate" follow:
miles per hour (mph). How many miles are covered in 1 hour of driving?
25 cents/pen: each pen costs 25 cents each.
Suppose I know I can pack 1/4 box in 20 minutes. How many boxes can I pack in 1 hour? That would be a unit rate. To find it, write out the ratio
1/4 box 60 min
------------- and multiply this by the conversion factor ---------------
20 min 1 hour
... which results in 3/4 box per hour (a unit rate)
The area of a triangle piece of stained glass is 50 centimeters if the height of the triangle is four times the base, how long are the height and base of the piece of stained glass
Answer:
Base = 5 cm
Height = 20 cm
Step-by-step explanation:
Points to remember
Area of triangle = bh/2
Where b - base of triangle
h - Height of triangle
To find the Height and Base of given triangle
It is given that,area of a triangle piece of stained glass is 50 centimeters
the height of the triangle is four times the base
h = 4b
Area = bh/2
50 = (b * 4b)/2
100 = 4b²
b² = 100/4 = 25
b =√25 = ±5
b = 5 then h = 4b = 4 * 5 = 20
Base = 5 cm and Height = 20 cm
ANSWER
base=5 cm, height = 20cm
EXPLANATION
The area of a triangle is
[tex]A = \frac{1}{2} bh[/tex]
From the question, A=50 and h=4b
We substitute into the formula to get;
[tex] \frac{1}{2} b \times 4b =5 0[/tex]
This implies that,
[tex]2 {b}^{2} = 50[/tex]
[tex] {b}^{2} = 25[/tex]
Take positive square root to get;
[tex]b = \sqrt{25} [/tex]
[tex]b = 5[/tex]
The base is 5 cm and the height is 20 cm.
The experiment is to roll a six-sided did with the dots
Answer:
1/2
Step-by-step explanation:
The answer is 1/2 because there are 3 even numbers and there are a total of six numbers which is 3/6 and when simplified it is 1/2.
Hoped this helped!
Please help me this is my worse subject
Answer:
it is the second answer choice
Step-by-step explanation:
hope it helps!
Hello!
-7 will be your answer.
Let’s first substitute in each of the choices below.
-17+-5 Does Not equal -12 so we know it’s not The first one
-7+-5=-12 We have our Answer but let’s just check the others just so we know.
7+-5 is the same thing as 7-5 so it will be 2.
And 17+-5 is the same thing as subtracting 5 so that will be 12.
Our answer is the second one
Consider the two functions shown below.
ANSWER
B. The functions f(x) and g(x) because f(g(x))=g(f(x))=x
EXPLANATION
The given functions are:
[tex]f(x) = 2x - 2[/tex]
and
[tex]g(x) = \frac{1}{2}x + 1[/tex]
If f(x) and g(x) are inverses, then
f(g(x))=x
[tex]f(g(x))=f( \frac{1}{2} x + 1)[/tex]
[tex]f(g(x))=2( \frac{1}{2}x + 1) - 2[/tex]
Expand the parenthesis to obtain,
[tex]f(g(x))=x + 2- 2[/tex]
[tex]f(g(x))=x[/tex]
Also,
[tex]g(f(x)) = g(2x - 2)[/tex]
[tex]g(f(x)) = \frac{1}{2} (2x - 2) + 1[/tex]
[tex]g(f(x)) = x - 1+ 1[/tex]
[tex]g(f(x)) = x [/tex]
Hence f(x) and g(x) are inverses
Answer: Option B
Then The functions f(x) and g(x) are inverses because [tex]f(g(x))=g(f(x))=x[/tex]
Step-by-step explanation:
To answer this question we must make the composition of f (x) and g (x)
We found
[tex]f (g(x))[/tex]
We know that
[tex]f(x) = 2x-2\\\\g(x) = \frac{1}{2}x + 1[/tex]
By definition if two functions f and g are inverses then it follows that:
[tex]f(g(x)) = g(f(x)) = x[/tex]
So if [tex]f(g(x)) = x[/tex] f and g are inverse
To find [tex]f(g(x))[/tex] enter the function g(x) within the function f(x) as shown below
[tex]f(g(x))= 2( \frac{1}{2}x + 1)-2\\\\f(g(x))= x + 2 -2\\\\f(g(x))= x[/tex]
Now
[tex]g(f(x))= \frac{1}{2}(2x-2) + 1\\\\g(f(x))= x-1 + 1\\\\g(f(x))= x[/tex]
Observe that
[tex]f(g(x))=g(f(x))=x[/tex]
Then The functions f(x) and g(x) are inverses because [tex]f(g(x))=g(f(x))=x[/tex]
Plsssss help !!!!!! At certain traffic light 10% of the cars passed through have four wheel drive what percentage do not have four wheel drive? Apex
Answer:
90%
Step-by-step explanation:
If you are going to find out the percent of the car that do not have 4 wheel drive, you take the total amount of car that passed though the stoplight which is 100% . You take this 100% and then subtract the 10% to get the final answer 90%. 90% of the cars do not have 4 wheel drive.
To find the percentage of cars without four-wheel drive, subtract the percentage of cars with four-wheel drive from the total. Since 10% of cars have four-wheel drive, 90% do not.
If 10% of the cars have four-wheel drive, then the percentage of cars without four-wheel drive is the remainder when the total percentage (100%) is reduced by the percentage of those that do have four-wheel drive.
To calculate this, we subtract the percentage of cars with four-wheel drive from the total percentage:
100% - 10% = 90%
Therefore, 90% of the cars do not have four-wheel drive.
A paper cup in the shape of an inverted cone is 6 inches tall and has a diameter of 3 inches.
V = 1/3π(1.5^2)(6)
How much water can the cup hold? Round to the nearest tenth.
A) 9.4
B) 14.1
C) 18.9
D) 56.6
Answer:
14.1 in³
Step-by-step explanation:
Your expression for the volume was correct, except that it lacked units of measurement.
The volume is V = (1/3)π(1.5 in)²(6 in) = 14.1 in³
The volume of the cup will be 14.1 cubic inches. Thus, the correct option is B.
What is the volume of the cone?Let h be the height of the cone and A be the base area of the cone. Then the volume of the cone will be given as,
V = 1/3 × πr²h
A paper cup in the shape of an inverted cone is 6 inches tall and 3 inches in diameter.
The volume of the cup is calculated as,
V = 1/3 × π(1.5)²(6)
V = 14.1 cubic inches
Thus, the correct option is B.
More about the volume of the cone link is given below.
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What is the value of x?
3cm
4cm
5cm
4.5cm
Answer:
5 cmStep-by-step explanation:
The triangles are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{x}{40}=\dfrac{4}{32}[/tex] cross multiply
[tex]32x=(40)(4)[/tex]
[tex]32x=160[/tex] divide both sides by 32
[tex]x=5[/tex]
Which is greater 2 2/3, 2.45, 2 2/5
This is least to greatest
2 2/5 or 2.40
2.45
2 2/3
2 2/5 , 2.45 , 2 2/3
Answer:
2 2/3
Step-by-step explanation:
2 2/3 = 2.666...
2.45 = 2.45
2 2/5 = 2.4
From least to greatest:
2 2/5, 2.45, 2 2/3
The greatest of the three numbers is 2 2/3
A rectangle has a perimeter of 48 feet and a length of 14 feet. Which equation can you solve to find the width?
Answer:
48=14+2w
An equation for this with no values would be 2w+2l=p
Step-by-step explanation:
I hope this helps if it does please add brainliest
Help fast please!!! Find the missing lengths of the sides.
Answer:
a = 12 ft, b = 12 ft
Step-by-step explanation:
The triangle is 45 45 90 right triangle
so a = b
Ratio of leg : hypo. = a : a√2
Given hypo = 12√2, so legs a = b = 12
Answer
a = 12 ft, b = 12 ft
A building is 120 meters tall. A scale model of the building uses a scale of 1 centimeter = 6 meters. How tall is the model?
Answer:
20 cm
Step-by-step explanation:
If the scale says that the building uses the scale or 1 cm: 6 meters. You pretty much just take 120 and divide by 6. You take that answer and turn the units in cm.
vincent uses 2 1/2 of flour for every 12 muffins that he makes what is the total number of cups of flour vincent will use to make 6 muffins
please show work on how you got the answer !
Answer:
1.25 cups or 1 1/4 cups
Step-by-step explanation:
Note that half of 12 muffins is 6 muffins.
If making 12 muffins requires 2.5 cups of flour, then halving both measurements results in 1.25 cups of flour per 6 muffins.
the ratio of participants on the girls track team to the number of boys on the track team is 5:7. If the boys have 22 more participants than the girls, how many girls are on the track team?
[tex]\bf girls:boys\qquad 5:7\qquad \cfrac{girls}{boys}=\cfrac{5}{7}\qquad ~\hspace{8em}\cfrac{\stackrel{\textit{girls}}{g}}{\underset{\textit{22 more than \underline{g}}}{g+22}}=\cfrac{5}{7} \\\\\\ 7g=5(g+22)\implies 7g=5g+110\implies 2g=110\implies g=\cfrac{110}{2}\implies g=55[/tex]
What is the perimeter of the shape? 40 feet 43 feet 51 feet 67feet
Answer:
26 is your answer.
Step-by-step explanation:
Perimeter is adding all the numbers around the shape up like: 11 + 3 + 6 + 3 + 3 = 26
Hope i have helped you!
Answer:
40 ft
Step-by-step explanation:
The perimeter of the shape is 1) the perimeter of the rectangle with sides of 11 and 3 ft plus 2) two sides of 6 ft each.
1) the perimeter of the rectangle: 22 + 6 = 28
2) the perimeter of two sides: 2x6= 12
3) The perimeter of the shape: 28 +12 =40
Put brackets in the following statement to make it true.
4+3x7-1=42
Answer:
(4+3)x(7-1)=42
The correct position of the brackets is [tex](4+3)*(7-1)=42[/tex].
The given equation is:
[tex]4+3*7-1=42[/tex]
⇒[tex](4+3)*(7-1)=42[/tex]
Let us consider LHS,
[tex](4+3)*(7-1)[/tex]
[tex]=7*(7-1)[/tex]
[tex]=7*6[/tex]
[tex]=42[/tex]
[tex]=RHS[/tex]
Hence, the above position of the bracket in the given statement is making it true.
Therefore, the correct position of the bracket is [tex](4+3)*(7-1)=42[/tex].
What is the bracket?Brackets, in math, are a set of marks like parentheses that are used to enclose a set of terms. These terms may be within an algebraic expression, and in this case, the brackets are used to separate terms and denote the order of operations.
What do the [] brackets mean?Square brackets (also called brackets, especially in American English) are mainly used to enclose words added by someone other than the original writer or speaker, typically in order to clarify the situation: He [the police officer] can't prove they did it.
What is a bracket symbol?Different symbols like these: (, ), [, ], {, and } in your math books. These symbols are called brackets. Brackets in mathematics serve a very important purpose; these symbols help us group different expressions or numbers together.
Learn more about brackets, refer to:
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