Answer:
B) 8 students like both
===========================
Let the numbers be:
M - likes math, M = 17;E - likes English, E = 19;B - likes both, B is unknown;T- total number, T = 28.Since both M and E include B, we can show the total as:
Math only + English only + Both = Totaland
Math only = M - BEnglish only = E - BThe total can be expressed as:
M - B + E - B + B = T M + E - B = TSubstitute values and solve for B:
17 + 19 - B = 2836 - B = 28B = 36 - 28B = 8This is matching the answer choice B)
Maths be A and English be B
A+B-A[tex]\cap[/tex] B=AUBA intersection B be X
(A-X)+(B-X)+X=AUBA+B-X=2817+18-X=1835-X=28X=8Option B
At a party, 75% of the people are adults and 25% are children. What is the simplest ratio of adults to children?
0.3:0.1
Step-by-step explanation:
first convert the % to decimals.
75%=0.75
25%=0.25
then look for a common factor and divide be that, in this case its 5.
0.75/5=0.15
0.25/5=0.5
now since these arent in the simplified form, you gotta divide again by 5.
0.15/5=0.3
0.5/5=0.1
The ratio to adults to children is 3:1
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
75% of the people are adults and 25% are children.
So, the ratio of adult to children
= (75%) / (25%)
= 0.75 / 0.25
= 75/25
= 3/1
Hence, the ratio to adults to children is 3:1
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Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1).
The true statement is (b) use of incorrect header
How to determine the true statement?The product expression is given as:
(-2x - 1)(2x - 1)
Expand the expression
(-x - x - 1)(x + x - 1)
This means that the header of the algebra tiles would be:
-x, -x, 1 and x, x and -1
From the figure, we can see that this is incorrectly represented
Hence, the true statement is (b)
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Radical Equations: How do I solve this?
Answer:
(B). roots
Step-by-step explanation:
(a ± b)² = a² ± 2ab + b²
~~~~~~~~
( [tex]\sqrt{4x+5}[/tex] - [tex]\sqrt{x-1}[/tex] )² = ( [tex]\sqrt{x+4}[/tex] )²
( [tex]\sqrt{4x+5}[/tex] )² - 2[tex]\sqrt{(4x+5)(x-1)}[/tex] + ( [tex]\sqrt{x-1}[/tex] )² = ( [tex]\sqrt{x+4}[/tex] )²
4x + 5 - 2[tex]\sqrt{(4x+5)(x-1)}[/tex] + x - 1 = x + 4
2[tex]\sqrt{(4x+5)(x-1)}[/tex] = 4x + 5 + x - 1 - x - 4
[tex]\sqrt{(4x+5)(x-1)}[/tex] = 2x
( [tex]\sqrt{(4x+5)(x-1)}[/tex] )² = ( 2x )²
( 4x + 5 )( x - 1 ) = 4x²
4x² + x - 5 = 4x² ⇒ x = 5
What is a difference of squares that has a factor of x+8?
Ox²2-4
Ox²-16
O²-64
Ox²-256
Answer :
X*2-16
Explanation :
The square of x is x*2 and the square of 8 is 64
The product of two number is 8 . If one of the numbers is 3 1/3 find the other number.
Hello!
Let the missing number be x.
⇒ 3 1/3 × x = 8
⇒ 10/3 × x = 8
⇒ x = 24/10
⇒ x = 12/5
The other number is [tex]\boxed {\frac{12}{5}}[/tex]
Answer:
The other number ia:
12/5
Step-by-step explanation:
3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3
a * 10/3 = 8
a = 8*3/10
a = 24/10
a = 12/5
a = 2.4
Check:
(12/5) * (10/3) = 8
(12*10) / (5*3) = 8
120 / 15 = 8
One half of 8 5/9 is
Answer:
Step-by-step explanation:
Answer:
4 5/18 ≈ 4.278
Step-by-step explanation:
1/2 of 8 5/9
8 5/9 = 77/9
1/2 x 77/9
= 77 over 18
= 77/18
= 4 and 5/18
≈ 4.278
Hope this helps!
The total cost for tuition plus room and board at State University is $2,584.00. Tuition costs $100 more than twice room and board. How much is the cost of room and board at State University?
Answer:
$1756
Step-by-step explanation:
1. More = Addition
2. Twice = Multiplication by 2
3. Tuition costs $100 more than twice room and board
Tuition = 2x + 100
$2584 = (2x + 100) + x
$2584 = 3x + 100
4. Subtract 100 on both sides: $2484 = 3x
5. Divide both sides by 3: $828 = x
6. Plug it in to the tuition equation: Tuition = 2(828) + 100
= $1756
Check Work: (828*2) + 100 = $1756
$1756 + 828 = $2584
Figure ABCDE has an area of 26 cm/. ABD and CBE are straight lines.
Find the area of the shaded triangle BDE,
The area of the shaded triangle BDE is 4 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape.
area of ΔADE= / *b *h
=1/2 * 8 *5
= 20 cm²
area of ΔBCD
= 26-20
= 6 cm²
area of CDE
= 1/2* 5 * 4
= 10 cm²
Area of shaded triangle,
=10-6
=4 cm²
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Please help me....trying to get my HS diploma, i did not graduate :(
A ball is thrown in air and it's height, h(t) in feet, at any time, t in seconds, is represented by the equation h(t)=−t2+7t. When is the ball higher than 10 feet off the ground?
A. 2
B. −5≤t≤−2
C. 2≤t≤5
D. −5
When t is between 2 and 5, the ball will be above 10 feet.so answer is:
C. 2 ≤ t ≤ 5
Given, height h(t) = ₋t² ₊ 7t
At what values of time t is the ball 10 feet above the ground = ?
To find out the time we need to set up an inequality.
Inequality expression is given as = ₋t² ₊ 7t ≥ 10
= ₋t² ₊ 7t ₋ 10 ≥ 0
= ₋(t² ₋ 7t ₊ 10) ≥ 0
= t² ₋ 7t ₊10 ≥ 0
Now, factorize the expression and get the factors.
= t² ₋ 2t ₋ 5t ₊ 10 ≥ 0
=t(t ₋ 2) ₋ 5(t ₋ 2) ≥ 0
=(t ₋ 2) (t ₋ 5) ≥ 0
Hence t value ranges from t = 2 and 5.
As a result, when t is between 2 and 5 seconds, the ball will be farther than 10 feet, 2 ≤ t ≤ 5
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Which is the graph of the line with equation y−6=4(x−3)+2?
Number graph ranging from negative four to three on the x axis and negative five to two on the y axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero).
Number graph ranging from negative three to three on the x axis and negative seven to one on the y axis. A line is drawn on the graph that passes through the points (zero, negative six) and (three, zero).
Number graph ranging from negative three to three on the x axis and negative two to five on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four).
Number graph ranging from negative three to three on the x axis and negative two to five on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, four).
The linear equation passes through (0, -4) and (1, 0), so we conclude that the correct option is the first one.
Which is the graph of the given linear equation?
Here we have the linear equation:
y - 6 = 4*(x - 3) + 2
if we rewrite the line in slope-intercept form, we get:
y = 4x - 12 + 2 + 6
y = 4x - 4
Then the y-intercept of the line is (0, -4). And when x = 1, we have:
y = 4*1 - 4 = 0
So the line also passes through (1, 0).
Then the correct option is the first one:
"Number graph ranging from negative four to three on the x-axis and negative five to two on the y-axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero)."
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graph F(x) = |x - 1|
Draw the graph:
f(x) = |x-1|
f(x) = -(x-1) when x-1 is negative
f(x) = (x-1) when x-1 is positive
when x = -2, f(x) = 3
when x = -1, f(x) = 2
when x = 0, f(x) = 1
when x = 1, f(x) = 0
when x = 2, f(x) = 1
Using this values, draw the graph of f(x) = |x-1|
Hence, the required modulus of x-1 graph.
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witch hazel is listed at 12 per galon, less 34.5%. what is the net cost of the amount needed in filling the prescription
The net cost of the amount needed in filling the prescription is 7.86 per gallon
Net costCost of witch hazel = 12 per gallonDiscount = 34.5%Net cost = 12 - (34.5% of 12)
= 12 - (0.345 × 12)
= 12 - 4.14
= 7.86 per gallon
Therefore the net cost of the amount needed in filling the prescription is 7.86 per gallon
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need help with this
The graph of R intersects with the horizontal or oblique asymptote at (-3, 0)
The horizontal asymptoteThe function is given as:
[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]
Set the numerator to 0
[tex]R(x)=\frac{0}{x\left(x+8\right)}[/tex]
Evaluate
R(x) = 0
This means that the horizontal asymptote of R(x) is y = 0
The oblique asymptoteThe function is given as:
[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]
The numerator has a degree of 1, while the denominator has a degree of 2
When the degree of the numerator is less than the degree of denominator, then the function has no oblique asymptote
Hence, the function has no oblique asymptote.
Intersection of the function and the horizontal asymptote
In (a), we have:
R(x) = 0
Substitute R(x) = 0 in [tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]
[tex]\frac{x+3}{x\left(x+8\right)} = 0[/tex]
Cross multiply
x + 3 = 0
Solve for x
x = -3
So, we have:
(x, y) = (-3, 0)
Hence, the graph of R intersects with the horizontal or oblique asymptote at (-3, 0)
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1. How many variables are involved in the chi-square test?
2. Which type of chi-square test is this?
A.goodness of fit B.test of independence
3. How many degrees of freedom are involved?
4. Using the chi-square critical values table is the result of this rest statistically significant?
A. Yes B.No
The result of the respective questions are:
This chi-square test only takes into consideration one variable.The type of chi-square test this is is a Goodness of Fitdf= 3NOHow many variables are involved in the chi-square test?a)
This chi-square test only takes into consideration one variable.
b)
The type of chi-square test this is, is a Goodness of Fit
To test the hypothesis, we must determine whether the actual data conform to the assumed distribution.
The "Goodness-of-Fit" test is a statistical hypothesis test that determines how well the data that was seen resembles the data that was predicted.
c)
Parameter
n = 4
Therefore
Degrees of freedom
df= n - 1
df= 4 - 1
df= 3
d)
In conclusion
Parameters
[tex]\alpha = 0.05[/tex]
df = 3
Hence
Critical value = 7.814728
Test statistic = 6.6
Test statistic < Critical value, .
NO, the result of this test is not statistically significant.
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Find an equation of the line passing through the given points. Use function notation to write the equation,
(-4,9) and (2,-3)
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1 z=-0.92 z=1.23
The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
1.) The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.
2.) The area of the shaded region for a z-score of 1.23 is 0.8907, which means the area that will be shadeded in the normal distribution graph is 89.07% of the total.
Now, the area of the shaded region will be,
Area = 0.8907 - 0.1788
= 0.7119
= 71.19%
Hence, the area of the shaded region is 71.19%.
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Find the probability of rolling a sum of 7 or 11. (sum of 7 or 11) = _______________
b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) = ______________
c. Find the odds against rolling a sum of 7 or 11.
d. In gambling the “odds against” (or “odds on”) usually expresses how much you can gain with a win for each
dollar you bet. If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11,
how much money will you win? Include your winnings plus your initial bet.
a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11) is 2/9. b. the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) is 7/9.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The probability of getting a total of 7 = 6/36
The probability of getting total of 11 = 2/36
a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11)
= 6/36 + 2/36
= 2/9
b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11)
= 1- 2/ 9
= 7/9
c. Find the odds against rolling a sum of 7 or 11.
= 2/9
d. The money you will win, If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11.
10 x 2/9 = 20/9
10 x 7/9 = 70/9
Thus, The money you will win $10.
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Translate the following from words to an algebraic expression or equation,
denoting the unknown by n.
52a. The express train travels 5 mph faster than the local train.
52b. The length of a rectangle is 7 inches more than its width.
52c. The area of a triangle, if the altitude is twice the base
52d. The sum of 3 consecutive even numbers
52e. 15% of the amount by which a number exceeds 10,000
Answer:
a. n+5
b. n+ 7
c. 1\2(n×2n)
d. n +n+1 n+2
Help, please
A rectangular room is 1.2 times as long as it is wide, and its perimeter is
30 meters. Find the dimension of the room.
length___
Width is____
The width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Let the width of the rectangle be x.
Given that a rectangular room is 1.2 times as long as it is wide. Therefore, the length is 1.2x.
Perimeter = 2(x + 1.2x)
30 meters = 2(2.2x)
30 = 4.4x
x = 6.82
Hence, the width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.
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Q. Unscramble the following term related to algebra:- ROTPORAE.
Answer:
operator
Step-by-step explanation:
Operator is represented as any symbol that indicates an operation to be performed.
Examples:
- Square root of√x, which indicates the square root is to be taken
- d/dx, which indicates differentiation with respect to x is to be performed
Answer:
OPERATION
OF ALGEBRA IN MATH
x/4 + 10 = 1
Please include steps
Answer:
x = -36
Step-by-step explanation:
x/4 + 10 = 1
To solve this two step equation, first subtract 10 from each side.
x/4 + 10 -10 = 1-10
x/4 = -9
Then multiply each side by 4 to isolate x
x/4 * 4 = -9*4
x = -36
yolanda drove 638 miles in 11 hours at the same rate how many miles would she drive in 13 hours
Answer: 754
Step-by-step explanation:
Divide 683/11 to get the unit rate of 58. That means she is driving 58mph.
Multiply that by how many hours you have, 13, and you get 754.
I need to find side c
The value of the hypotenuse is C = 11.73
How to find the value of C?
We can see that C is the hypotenuse of the right triangle.
We can see that the top angle measures 43°, and the opposite cathetus to that angle measures 8 units.
Then we can use the rule:
Sin(a) = (opposite cathetus)/(hypotenuse).
Replacing what we know:
Sin(43°) = 8/C
Solving for C:
C = 8/Sin(43°) = 11.73
The value of the hypotenuse is C = 11.73
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Simplify.
1/4(3x-7)+3/4x
Answer:
C. [tex]1\frac{1}{2} x - 1\frac{3}{4}[/tex]
Step-by-step explanation:
c
Answer:
[tex]1\frac{1}{2}x - 1\frac{3}{4}[/tex]
Step-by-step explanation:
So the first step is to distribute the [tex]\frac{1}{4}[/tex] to the (3x - 7) this gives you:
[tex]\frac{3}{4}x-\frac{7}{4} + \frac{3}{4}x[/tex]
Add like terms:
[tex]\frac{6}{4}x-\frac{7}{4}[/tex]
Simplify the fractions:
[tex]\frac{3}{2}x-\frac{7}{4}[/tex]
Convert it to a mixed fraction:
[tex]1\frac{1}{2}x - 1\frac{3}{4}[/tex]
The number of people who attend a concert varies directly with the amount of money spent on advertising. If tickets are sold when is spent on advertising, how much money needs to be spent on advertisements to get a sellout crowd of 1500?
Answer:
refer to the above attachment
What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months? a. $25.47 b. $202.55 c. $611.20 d. $4,861.20 please select the best answer from the choices provided a b c d
The total finance charge is $611.20 (Option c) for this compound interest.
Data Given
Principal, P = $4250
Rate of Compound Interest, R = 13.25%
Time, t = 24 months, i.e., 2 years
Since it is compounded monthly, n = 12
Calculating the Total Finance Charge
We know that the formula for total amount of finance charge in a Compound Interest is,
[tex]A=P\frac{r(1+r)^{n} }{(1+r)^{n} - 1}[/tex]
Substituting the values of P, R and n, we get,
[tex]A=4250\frac{13.25(1+13.25)^{24} }{(1+13.25)^{24} - 1}[/tex]
[tex]A = 611.20[/tex]
Thus, the total finance charge is $611.20
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Find the equation of the plane passing through the points A=(1,1,1), B=(1,4,5), C=(−3,-2,0).
Find the area of the triangle the 3 points from the first equation.
Find the angle between the 2 vectors; (1) from A to B and (2) from C to B.
Take any two pairs of the given points and make vectors out of them. For example, the vector from A to B is
[tex]\vec v_1 = \langle 1,4,5\rangle - \langle 1,1,1\rangle = \langle0,3,4\rangle[/tex]
and the vector from A to C is
[tex]\vec v_2 = \langle -3,-2,0\rangle - \langle1,1,1\rangle = \langle-4,-3,-1\rangle[/tex]
These vectors lie in the same plane (the one we want). We can get a third vector that is normal to the plane by taking their cross product (details omitted).
[tex]\vec n = \vec v_1 \times \vec v_2 = \langle 9,-16,12 \rangle[/tex]
If [tex]\vec u = \langle x,y,z\rangle[/tex] is an arbitrary vector, then the vector from any of the points A, B, or C to [tex]\vec u[/tex] will lie in our plane. That is, if we start from A,
[tex](\vec u - \langle1,1,1\rangle) \cdot \vec n = 0[/tex]
and this reduces to the equation of the plane,
[tex]\langle x - 1, y - 1, z - 1 \rangle \cdot \langle 9, -16, 12 \rangle = 0[/tex]
[tex]9 (x - 1) - 16 (y - 1) + 12 (z - 1) = 0[/tex]
[tex]\boxed{9x - 16y + 12z = 5}[/tex]
Area of triangle ABCThis follows immediately from the cross product identity
[tex]\|\vec x \times \vec y\| = \|\vec x\| \|\vec y\| \sin(\theta)[/tex]
where [tex]\theta[/tex] is the angle between [tex]\vec x[/tex] and [tex]\vec y[/tex]. The left side corresponds to the area of the parallelogram spanned by [tex]\vec x[/tex] and [tex]\vec y[/tex]; half of this area would be that of a triangle. (see attached)
In our case, we have
[tex]\|\vec n\| = \|\vec v_1 \times \vec v_2\| = \sqrt{481}[/tex]
so the area of ABC is [tex]\boxed{\dfrac{\sqrt{481}}2}[/tex].
Angle between A to B and between C to BWe already know the first vector, [tex]v_1[/tex].
The vector from C to B is
[tex]\vec v_3 = \langle 1,4,5 \rangle - \langle -3,-2,0 \rangle = \langle 4, 6, 5 \rangle[/tex]
Recall the dot product identity,
[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]
Then
[tex]\vec v_1 \cdot \vec v_3 = \|\vec v_1\| \|\vec v_3\| \cos(\theta) \implies \cos(\theta) = \dfrac{38}{5\sqrt{77}} \implies \theta \approx \boxed{29.9914^\circ}[/tex]
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget: 2,020 − 22m
What does the coefficient of the expression represent? The number of months Megan will wait to sell the gadget The monthly depreciation value of the gadget The amount of money Megan will get when she sells the gadget The original value of the gadget
The coefficient (m) of the expression represents: C. the monthly depreciation value of the gadget.
What is depreciation?Depreciation can be defined as a process in which the monetary value of a physical asset decreases or falls over a period of time, especially due to wear and tear.
In this scenario, we can infer and logically deduce that the coefficient (m) of the given expression represents the monthly depreciation value of Megan's gadget.
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Answer:
it is C
Step-by-step explanation:
give the other guy brainliest, I am ok with hearts and good ratings.
100POINTS WHY NOT
sally took money from her bank account to go out of town for an audition.she spot 54$ for a round trip ticket and 1/2 of the remaining money on her hotel bill.she spent $7.90 for food and arrived home with $15.10.How much money did Sally take from her bank account??
Answer:
$100
Step-by-step explanation:
Given information:
$54 = cost of ticketCost of hotel = 1/2 remaining money after purchase of ticket$7.90 = cost of food$15.10 = remaining moneyLet x = money taken from bank account
If Sally paid $54 for her ticket, then the money remaining at that point can be defined as: [tex]x-54[/tex]
If the cost of the hotel was half of the remaining money, then:
[tex]\textsf{Cost of hotel}=\dfrac{1}{2}(x-54)}[/tex]
To find how much money Sally took from her bank account, create an equation with the given information and solve for x.
[tex]\implies \textsf{Money in bank} - \textsf{ticket} - \textsf{hotel} - \textsf{ food} =\textsf{remaining money}[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}(x - 54)-7.90=15.10[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}x+27-7.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x-34.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x=50[/tex]
[tex]\implies x=100[/tex]
Therefore, Sally took $100 from her bank account.
solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?
Answer:
Step-by-step explanation:
cos (x/2)=cos x+1
cos (x/2)=2cos ²(x/2)
2 cos²(x/2)-cos (x/2)=0
cos (x/2)[2 cos (x/2)-1]=0
cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)
x/2=2nπ+π/2,2nπ+3π/2
x=4nπ+π,4nπ+3π
n=0,1,2,...
x=π,3π
or x=180°,540°,...
180°∈[0,360]
so x=180°
or
2cos(x/2)-1=0
cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)
x/2=360n+60,360n+300
x=720n+120,720n+300
n=0,1,2,...
x=120,300,840,1020,...
only 120° and 300° ∈[0,360°]
Hence x=120°,180°,300°