Answer:
190
Step-by-step explanation:
40/100 x 198= 76
40/100 x 198= 114
114-76= 38
Answer:
190.
Step-by-step explanation:
Let x represent total number of votes.
We have been given that Joel got 60% of the votes, which was 38 votes more than Sean.
60% of total votes: [tex]\frac{60}{100}x=0.60x[/tex]
Since Joel got 60% of total votes, so Sean got 40% of total votes that is [tex]\frac{40}{100}x=0.40x[/tex]
Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:
[tex]0.60x=0.40x+38[/tex]
[tex]0.60x-0.40x=0.40x-0.40x+38[/tex]
[tex]0.20x=38[/tex]
[tex]\frac{0.20x}{.20}=\frac{38}{.20}[/tex]
[tex]x=190[/tex]
Therefore, the total number of votes cast is 190.
I need help with #63
Step-by-step explanation:
Given that line a is parallel to line b
∠6 = ∠2 = 36.5° (property of corresponding angles)
∠8 = 180° -∠6 (property of adjacent angles on a straight line)
∠8 = 180° - 36.5° = 143.5°
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1375 . How long did each mechanic work?
Answer:
Mechanic A worked for 5 hours and Mechanic B worked for 15 hours
I hope my answer and explanation helped!
okay to get started you need to make a system of equations:
x= number of hours worked by mechanic A
y= number of hours worked by mechanic B
x + y= 20
95x + 60y= 1375
substitute in an equation:
x + y= 20
y= 20- x
95x + 60(20-x)=1375
Solve for x
95x + 1200 - 60x=1375
35x =175
x= 5
plug in x to solve for y
x + y= 20
5 + y= 20
y=15
Check work
then you're done :D
What value of x is in the solution set of 9(2x + 1) < 9x – 18?.
Answer:
x < -3
Step-by-step explanation:
using the distributive property, distribute 9(2x +1) so it's 18x + 9, subtract 9x from 18x, subtract 9 from -18, divide both sides by 9, x < -3
Inequality is a relationship between two numbers or two expressions.
The value of x in the solution set of 9(2x + 1) < 9x – 18 is
x < -3
i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
9(2x + 1) < 9x – 18
Remove the parenthesis.
9 x (2x) + 9 x 1 < 9x - 18
18x + 9 < 9x - 18
Subtract 9x on both sides.
18x + 9 - 9x < 9x - 18 - 9x
9x + 9 < -18
Subtract 9 on both sides.
9x + 9 - 9 < -18 - 9
9x < -27
Divide both sides by 9.
9x/9 < -27/9
x < -3
This means x is less than -3.
i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞
Thus,
The value of x in the solution set is x < -3.
i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞
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Which of the following correctly describes the variation in the equation h= V/lw
Answer:
It shows that h varies directly with V and inversely with l and w.
Step-by-step explanation:
The given equation is:
h = V/lw
It shows that h varies directly with V and inversely with l and w.
Inversely means if the value of one entity increases, the value of second entity decreases or vice versa. Directly related means as one quantity increases, another quantity increases at the same rate
We can show it as h=1/lw which means h is in inverse relation with l and w and in direct relation with V....
members of the garner high school yearbook committe need to but 1,344 student photos on 24 pages in the yearbook. They want to put the same number of student photos on each page
What is an equation of the line that is perpendicular to y- 4 = 2(x-6) and
passes through the point (-3,-5)?
O A. y + 5 = 2(x+3)
O B. y-5=-2(x-3)
O C. v-5-x-3)
OD. y +5 - -}(x+3)
Answer:
D. Y+5=-(1/2)*(x+3)
Step-by-step explanation:
Perpendicular Lines are those with the following condition:
y=a*x+b (1)
y=c*x+d (2)
Where 'a' and 'c' are the respective slope
If These two lines are perpendicular, then
a=- 1/c
Equation (1) for our case is written as y=2x-8, meaning that a=2 and b = -8
Using those principles we have that the slope for our needed line ('c') has to be -(1/2).
Now we most use the given point to find the remaining term of the equation (d) so, evaluate (-3,-5) in eq (2) to have this:
-5=(-1/2)*(-3)+d
resulting that d=-5-(3/2)
Eq (2) is written now as the following: y= (-1/2)*x - (5+3/2)
Rearranging terms, we have the following:
y+5=(-1/2)*x-(3/2)
where you can obtain a more pretty expression:
y+5=(-1/2)*(x+3)
In a survey, 4 out of 30 students reported that they walk to school. If there are 900 students in the school, how many walk to school?
Answer: 120 people
Step-by-step explanation: To do this problem, you want to find common denominators. The lowest common denominator is 900. So to get the denominator to 900 from 30, multiply it by 30. 30 x 30=900. Multiply 4 by 30. 4 x 30=120. Another way to do this is to set up a proportion. It would be 4/30=x/900. Cross multiply and solve for x. 3600=30x. X=120.
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Find the approximate area of a circle that has a diameter of 11 inches. Round your answer to the nearest hundredth.
A = ___ in.2
Answer:
A = 95.03in² or 95.03 ( rounded to the nearest hundredth )
Step-by-step explanation:
The approximate area of a circle that has a diameter of 11 inches, rounded to the nearest hundredth is 95.03.
Formula: A=1/4πd²
A=1
4πd^2=95.03.
4·π·11^2≈95.03318in²
Add the polynomials 6a-4b+c and 4a+c
Answer:
10a-4b+2c
Step-by-step explanation:
Answer:
10a -4b +2c
Step-by-step explanation:
6a-4b+c and 4a+c
6a-4b+c + 4a+c
Combine like terms
6a+4a + (-4b) + c+c
10a -4b +2c
In general, the point __is on the graph of the function f(x) = a.pl
Use the Quadratic Formula to solve the equation 4x^2−7=4x.
Select one:
a. x=−1/2+√2 or x=−1/2−√2
b. x=7/8+√133/8 or x=7/8-√133/8
c. x=1/2+√2 or x=1/2−√2
d. x=2+4√2 or x=2−4√2
Answer:
[tex]\large\boxed{x=\dfrac{1}{2}-\sqrt2\ or\ x=\dfrac{1}{2}+\sqrt2}[/tex]
Step-by-step explanation:
[tex]\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\\sqrt{b^2-4ac}=\sqrt{128}=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\\\\x=\dfrac{-(-4)\pm8\sqrt2}{(2)(4)}=\dfrac{4\pm8\sqrt2}{8}\qquad\text{simplify by 4}\\\\x=\dfrac{1\pm2\sqrt2}{2}\to x=\dfrac{1}{2}\pm\sqrt2[/tex]
Determine the factors of x^2 − 12x − 20. (5 points)
For this case we must factor the following expression:[tex]x ^ 2-12x-20[/tex]
We have that the expression cannot be factored with rational numbers.
On the other hand, we can find the zeros, applying the quadratic formula we have:[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 1\\b = -12\\c = -20[/tex]
[tex]x = \frac {- (- 12) \pm \sqrt {(- 12) ^ 2-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144 + 80}} {2}\\x = \frac {12 \pm \sqrt {224}} {2}\\x = \frac {12 \pm \sqrt {16 * 14}} {2}\\x = \frac {12 \pm4 \sqrt {14}} {2}[/tex]
Thus, the roots would be:
[tex]x_ {1} = 6 + 2 \sqrt {14}\\x_ {2} = 6-2 \sqrt {14}[/tex]
Answer:
the expression cannot be factored with rational numbers.
The factors of the given quadratic expression are: (x - 2) and (x - 10)
What are the factors of the quadratic expression?The quadratic expression is given as:
x² - 12x - 20
Now, to get the factors, we need to write as follows:
x² - 10x - 2x + 20
This can be factorized to get:
x(x - 10) - 2(x - 10)
= (x - 2)(x - 10)
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From a window, the angle of elevation of the top of a flagpole is 25°, and the angle of depression of the base of the
flagpole is 12°.How high is the flagpole if the window is in a building at a distance of 185 feet from the flagpole?
Answer:
125.59 feet
Step-by-step explanation:
(see attached)
PLS HELP ASAP What is the value of x?
a. 12 units
b. 15 units
c. 20 units
d. 25 units
ANSWER
a. 12 units
EXPLANATION
According to the altitude theorem, RT which is the altitude, is equal to the geometric mean of TQ and TS, the segments created by the foot of the altitude on the hypotenuse.
This implies that:
[tex]x = \sqrt{TQ \times TS} [/tex]
From the diagram, TQ=16 and TS=9.
We substitute these values and solve for x.
[tex]x = \sqrt{9 \times 16} [/tex]
[tex]x = \sqrt{144} [/tex]
[tex]x = 12[/tex]
Therefore x is 12 units.
The correct answer is A
Which inequality is shown above?
Find the area of the polygon
Answer:
65 units²
Step-by-step explanation:
The polygon is composed of a trapezium and a triangle
Trapezium QRSU has area (A)
A = 0.5 h (a + b)
where h is the perpendicular height and a, b are the parallel bases.
h = RS = 7 , a = RQ = 6 and b = SU = 8, so
A = 0.5 × 7 × (6 + 8) = 0.5 × 7 × 14 = 49 units²
Triangle STU has area ( A )
A = 0.5 bh ( b is the base and h the perpendicular height )
here b = SU = 8 and h = 4 ( distance from vertex T to the base SU), so
A = 0.5 × 8 × 4 = 16 units²
Total area = 49 + 16 = 65 units²
I really need help ASAP !!
Answer:
Graph 1: Consistent Dependent
Graph 2: Consistent Independent
Graph 3: Consistent Dependent
Graph 4: Inconsistent
Step-by-step explanation:
Consistent means they have at least one solution. So lines that intersect once or lines that intersect infinitely many times are both consistent systems.
If they are the system that has one solution they are considered independent.
If they are the system that has infinitely many solutions then are considered dependent.
Inconsistent means they won't intersect at all.
First graph shows the same line graphed onto itself. That means they have infinitely many solutions and is therefore a consistent dependent system.
Second graph shows the lines intersecting once. That means they have one solution and therefore is a consistent independent system.
Third graph shows the same description of graph one and is therefore a consistent dependent system.
The last graph shows parallel lines. Parallel lines do not intersect and therefore do not have a solution. So this system is inconsistent.
which statement is true regarding the graphed functions?
Answer:
A
Step-by-step explanation:
The graphs of two functions y=f(x) and y=g(x) intersect at one point. The coordinates of this point are (0,-2). This means
f(0)=-2
g(0)=-2
Thus,
f(0)=g(0)
Note that the blue line passes through the point (-2,4), so
f(-2)=4
and the red line passes through the point (-2,-4), so
g(-2)=-4
Hence,
f(-2)≠g(-2)
and f(0)≠g(-2)
Answer:
First Option
Step-by-step explanation:
It can be seen in the graph that the two plotted functions are linear, which means that if the lines are not parallel or not lying on each other, then the lines will intersect at most one point in the plane. It can be clearly seen that both the lines intersect at the point (0,-2). As far as the functions are concerned, there is an input and an associated output. The term f(0) means that 0 is the input and f(0) is the functional value, which is the output. In the graph, both lines have the y-intercept of -2. Y-intercept is the point where the value of the input (i.e. the value of x) is 0. Since both lines are intersecting at (0,-2), this implies that f(0) = g(0). This essentially means that the the functional value of f, which is -2, is equal to the functional value of g!!!
Evaluate f(x) = 1/4 x for x =-5.
Answer:
f(x) = -1.25
Step-by-step explanation:
Substitute x with -5, so our equation would look this:
Note: We were already given the value of x
f(x) = 1/4(-5)
Multiply 1/4 and -5:
1/4 * -5 = -1.25
So, our answer would be -1.25
-1.25
Step-by-step explanation:In order to find the answer to your question, we're going to need to plug in a number to the variable x.
We know that x = -5
This means that whenever you see x, you would replace it with what it equals to. In this case, we would plug in -5 to x, since that's what it equals to.
Your equation would look like this:
[tex]\frac{1}{4}( -5)[/tex]
Now, you would solve to get your answer.
[tex]\frac{1}{4} (-5)=-1.25\\\\\text{1/4 is the same as 0.25} \\\\0.25(-5)=-1.25[/tex]
Once you're done solving, you should get -1.25
This means that f(x) = -1.25
I hope this helps you out.Good luck on your academics.Have a fantastic day!If a sprinkler waters 1 over 15 of a lawn in 1 over 5 of an hour, how much time will it take to water the entire lawn? 2 hours 3 hours 10 hours 15 hours
Answer:
3 hours
Step-by-step explanation:
Hours/Lawn = (1/5 h)/(1/15 lawn) = 15/5 h/lawn = 3 h/lawn
It will take the sprinkler 3 hours to water the lawn.
Answer:
3 hours 100%
Step-by-step explanation:
What is the missing reason for the 3rd step in the proof below?
Answer: B
Step-by-step explanation:
Because m<7 and m<6 share a vertex and doesn’t share any common sides and they are across from each other which means they are vertical and vertical angles are congruent
The missing reason for the 3rd step will be vertical angles are congruent. Then the correct option is B.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
The diagram is given below.
Then the missing reason for the 3rd step will be vertical angles are congruent.
Thus, the correct option is B.
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A random sample of 145 students is chosen from a population of 4,250 students. If the mean IQ in the sample is 130 with a standard deviation of 7, what is the 90% confidence interval for the students' mean IQ score?
Answer:
125-135
Step-by-step explanation:
The standard deviation is 7. This implies that the IQ scorings can be between 123 and 137. With a 90% confidence in these numbers, 125-135 is the closest interval to 90% confidence.
Answer: (129.04,130.96)
Step-by-step explanation:
Given : Sample size : n= 145
Mean IQ in the sample : [tex]\overline{x}=130[/tex]
Standard deviation : [tex]\sigma=7[/tex]
Significance level : [tex]\alpha=1-0.9=0.1[/tex]
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=130\pm(1.645)\dfrac{7}{\sqrt{145}}\\\\=130\pm0.96\\\\=(129.04,\ 130.96)[/tex]
Hence, the 90% confidence interval for the students' mean IQ score is (129.04,130.96)
Figure ABCD is a parallelogram.
What are the lengths of line segments AB and BC?
○ AB=4; BC=16
○AB=4; BC=8
○AB=10; BC=20
○AB=10; BC=28
Answer:
○ AB = 10; BC = 28Step-by-step explanation:
In each parallelogram opposite sides have the same length.
Therefore we have the equations:
2x - 4 = x + 12 and 3y - 2 = y + 6
2x - 4 = x + 12 add 4 to both sides
2x = x + 16 subtract x from both sides
x = 16
3y - 2 = y + 6 add 2 to both sides
3y = y + 8 subtract y from both sides
2y = 8 divide both sides by 2
y = 4
AB = 3y - 2 → AB = 3(4) - 2 = 12 - 2 = 10
BC = x + 12 → BC = 16 + 12 = 28
Answer:
D
Step-by-step explanation:
Find an equation whose line is perpendicular
to the line on the graph.
y =2x+2
y = 2x + 7
y=-1/2x-7
y=1/2x+1
[tex]\huge{\boxed{y=\frac{1}{2} x+1}}[/tex]
First, we must find the slope of the graphed line. We can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are known points on the line.
Plug in the values. [tex]\frac{4-2}{-1-0}[/tex]
Subtract. [tex]\frac{2}{-1}[/tex]
Simplify. [tex]-2[/tex]
To find the slope of the perpendicular line, we must find the opposite inverse slope. This means we first need to multiply it by [tex]-1[/tex], then we need to swap the numerator and denominator.
[tex]-2*-1=2[/tex]
Now, swap the numerator and denominator. The numerator is [tex]2[/tex], and the denominator is [tex]1[/tex] by default.
[tex]\frac{1}{2}[/tex]
The only answer choice with a slope of [tex]\frac{1}{2}[/tex] is [tex]\boxed{y=\frac{1}{2} x+1}[/tex]
The function f(x) = 200(0.901), where x is the time in
years, models a declining lemming population. How
many lemmings will there be in 7 years?
Answer:
There will be 96 lemmings in 7 years
Step-by-step explanation:
we have
[tex]f(x)=200(0.901)^{x}[/tex]
This is a exponential function
where
x ------> the time in years
f(x) ----> lemming population
so
For x=7 years
substitute in the function
[tex]f(7)=200(0.901)^{7}[/tex]
[tex]f(7)=96.4[/tex]
There will be 96 lemmings in 7 years
NEED HELP QUICK! WILL GIVE BRAINLIEST AND 25 POINTS!!!!
Show the formula for finding the area of a parallelogram. Then find the area of the parallelogram pictured:
Answer:
611.04 mm³
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 30.4 and h = 20.1, hence
A = 30.4 × 20.1 = 611.04 mm³
Answer:
611.04 mm³
Step-by-step explanation:
Formula for finding the area of a parallelogram: A = B * H
B is base, H is height, * is multiply.
_________________________________________________
The area of the parallelogram pictured: 611.04 mm³
A=bh=30.4·20.1=611.04
_________________________________________________
which term can be used in the blank of 36x^3-22x^- so the greatest common factor of the resulting polynomial is 2x?
Final answer:
The missing term in the polynomial 36x³ - 22x + ___ that ensures a GCF of 2x must be ax, where 'a' is an even number. Possible terms could be 4x, -8x, or any other term with an even coefficient and an x factor.
Explanation:
The student's question asks which term can be used in place of the blank in the polynomial 36x³- 22x + ___ so that the greatest common factor (GCF) of the resulting polynomial is 2x. To determine the missing term, we need to look at the existing terms of the polynomial. The first term, 36x³, has a GCF of 2x because 36 is divisible by 2 and x³ has x as a factor. Similarly, the second term, -22x, also has a GCF of 2x since 22 is divisible by 2 and there's already an x present. To ensure that the GCF of the final term with the others is 2x, the term must have both a coefficient divisible by 2 and at least one factor of x.
Let's say the missing term is ax, where 'a' is an even number to keep the common factor of 2x. Therefore, a term like 4x or -8x could work. If the resulting polynomial had a term without x, then the GCF would just be 2, not 2x. Hence, adding a term with a factor of 2 and x not only completes the polynomial but also ensures that the GCF is 2x.
2 Points
What is the measure of the radius of OM?
A. 14.8 units
10.5
B. 10.5 units
10.5
c. 21.0 units
D. 5.25 units
Answer:
B. 10.5 units
Step-by-step explanation:
The radius of a circle is a segment that has the center of the circle as one endpoint and a point on the circle as the other endpoint. The length of a radius is also called radius.
The figure shows two radii: segments MR and MS.
The lengths of all radii of a circle are equal.
MR = MS = 10.5 units
Answer:
10.5 units
Step-by-step explanation:
The radius of Circle M is the distance from the center M to the circle
That is 10.5 units
The scale of a map is 1/8 = 10 miles. If 2 cities are 3 inches apart on the map, how many mikes are they from each other? A.) 24 B.) 80 C.) 120 D.) 240 E.) None of these
Answer:
D.) 240 miles.
Step-by-step explanation:
By proportion the distance between the 2 cities
= (3 / 1/8) * 10
= 3*8*10
= 240 miles.
The 2 cities are D.) 240 miles away.
By proportion of the distance between the 2 cities
= (3 / 1/8) * 10
= 3*8*10
= 240 miles.
What is the proportional distance?This means that in case your journey is twice as lengthy, you will move two times as a long way. in case you journey three times as long, you will pass 3 instances as a ways. At the same time as in case you tour half as long, you may go 1/2 as far. By something ratio the time adjustments, the distance will alternate proportionally, that is, within the identical ratio.
The made of approach within the ratio is identical to the made from extremes. Two ratios are stated to be identical if their cross products are identical. The sharing formula is given as, a : b :: c : d ⇒ a b = c d.
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which of the following could be the equation of the graph below? See graph below select the answer
ANSWER
[tex]y = 2( {x - 4)}^{2} - 3[/tex]
EXPLANATION
The function equation of a parabola that opens up in vertex form is given by
[tex]y = a( {x - h)}^{2} + k[/tex]
where (h,k) is the vertex and 'a' is the leading coefficient.
The given graph is a parabola that opens up and has its vertex at (4,-3).
This implies that, h=4 and y=-3
We substitute these values into the vertex form to obtain,
[tex]y =a( {x - 4)}^{2} + - 3[/tex]
This simplifies to,
[tex]y =a( {x - 4)}^{2} - 3[/tex]
The graph also contains (3,-1). We plug x=3 and y=-1 into the equation to find the value of 'a'.
[tex] - 1=a( {3 - 4)}^{2} - 3[/tex]
[tex] - 1 + 3 = a( { - 1})^{2} [/tex]
[tex]2 = a[/tex]
We substitute this value to get:
[tex]y = 2( {x - 4)}^{2} - 3[/tex]
The last choice is correct.