This is based off your understanding if you think you understand this method click A if not, D
A car averages 25 2/3
miles on a gallon of gas. How many miles can it travel on 8
Answer:
205 1/3
Step-by-step explanation:
Because it travels an average of 25 2/3 on one gallon, you simply multiply it by 8 in order to find how many miles it travels on 8 gallons of gas.
: 3a2 + 2b2 when a = -3 and b = 6
Answer: 63
Step-by-step explanation:
3(-3)^2 + 2(6)^2 (multiply 3 times -3) & (multiply 2 times 6)
-9^2+12^2 (-9 to the 2nd power and 12 to the 2nd power)
-81+144 (add them up)
=63
The value of the expression is 3a² + 2b² is 69.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 3a² + 2b²
Not, put the value of a= -3 and b=6 we get
= 3a² + 2b²
= 3(-3)² + 2(4)²
= 3 x 9 + 2 x 16
= 37 + 32
= 69
Hence, the value of expression is 69.
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Latoya got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 17
cents per yard. If after that purchase there was $8.88 left on the card, how many yards of ribbon did Latoya buy?
Answer: 36 yards
Step-by-step explanation:
Determine how much was spent.
15-8.88= $6.12
Each yard was 17 cents and $6.12 was spent.
6.12/.17= 36
(Amount spent/Cost per yard)= Amount of ribbon (in yards)
36 yards
in how many ways cab four men and four ladies be seated at a round ravke uf no two men are to be in adjacent seats
In 144 ways can four men and four ladies be seated at a round table such that no two men are to be in adjacent seats.
In the given question we have to check in how many ways can four men and four ladies be seated at a round table such that no two men are to be in adjacent seats.
4 men and 4 ladies have to sit in the round table.
No two men should sit together.
So first we arrange 4 ladies in the round table. We arrange 4 ladies in the round table in four direction and the we get four places left in the middle of two women. Then we can arrange the 4 men there.
To make 4 ladies to sit in round table = (4-1)!
To make 4 ladies to sit in round table = 3!
To make 4 ladies to sit in round table = 6 ways
Now 4 men in gaps can be arranged in 4! = 24 ways
Hence, total number of ways = 6*24
Total number of ways = 144 ways
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B.y = 4x + 2
y = -8x + 8
Answer: \(x=\frac{1}{2}, y=4\)
Step-by-step explanation:
Setting the equations equal to each other,
\(4x+2=-8x+8\\\\12x+2=8\\\\12x=6\\\\x=\frac{1}{2}\)
This means \(y=4\left(\frac{1}{2} \right)+2=4\)
So, the solution is \(\boxed{x=\frac{1}{2}, y=4}\)
Please see photo I think it is the first answer but I wanted to confirm
Hello
The sample which she has to study is 200
The answer to this question is option A
What's the mean of data set 15, 17, 23, 19,
Step-by-step explanation:
15 + 17 + 23 + 19
32 + 42 = 74
74/4 = 18.5 is the mean
Answer:
Mean= 18.5
Step-by-step explanation:
How to Find the Mean
Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count
The mean is the same as the average value in a data set.
Mean Formula
The mean x of a data set is the sum of all the data divided by the count n.
Angle A is circumscribed about circle O.
What is the measure of
Answer:
\( m\angle O = 134 \degree\)
Step-by-step explanation:
AC and AB are tangents to the circle with center O on points C and B respectively from point A.
Therefore
\( m\angle ACO=m\angle ABO=90\degree \)
\( m\angle CAB=46...(given) \degree \)
\(m\angle O = 360 \degree - (2 \times 90 \degree + 46 \degree) \\ \\ m\angle O = 360 \degree - (180 \degree + 46 \degree) \\ \\ m\angle O = 360 \degree - (226 \degree) \\ \\ m\angle O = 134 \degree\\ \\ \)
pleas
HELP IMMEDIATELY
Answer:
144ft^3
Step-by-step explanation:
To start, we have your formula: \(V=\frac{1}{2} (bh) (l)\)
b = base length of the triangle.
h = height of the triangle.
l = length of the prism
Fill in for each of those values:
\(V = \frac{1}{2} (6x6)(8)\)
\(V=\frac{1}{2} (36)(8)\)
\(V=(18)(8)\)
\(V=144\)
Your answer, because it is a 3D shape, should be cubed, so:
\(V=144ft^{3}\)
Please help urgent thank you
If he wants an average of 84, he needs to get at least 93 points.
What score does he need to get in the next test?Remember that the average value between 3 values A, B, and C is:
(A + B + C)/3
Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:
(76 + 83 + x)/3 = 84
159 + x = 252
x = 252 - 159
x = 93
So he needs to get at least 93 points in the next exam.
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Please answer this question now in two minutes
Answer:
ray UV and ray UT
Step-by-step explanation:
The sides are the rays that make up the angle
ray UV and ray UT make up the angle VUT
Value of x or y so that the line through the points has the given slope:
(X,9) and (9,-3), slope is -6/7
Sorry if it’s not worded great.
If we want the slope to be -6/7, then the value of x must be -5.
How to find the value of x?Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:
\(a = \frac{y_2 - y_1}{x_2 - x_1}\)
Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:
\(\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}\)
Where on the second line we multiplied and divided the right fraction by 2.
Comparing the fractions, we see that we must have:
9 -x = 14
9 - 14 = x
-5 = x
So the value of x must be -5.
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Guys I’m confused I need help plz
Answer:
EG = 41
Step-by-step explanation:
since angles E and G are equal, the sides opposite them are equal
5x+23 = 7x+9
23 = 2x+9
14 = 2x
7 = x
EG = 6x-1
substitute 7 for 'x' to get:
EG = 6(7)-1 = 41
A customer returns a $35.50 item to a store. In th
$52.40, including tax.
How much does the customer pay?
$16.00
$16.90
O $18.60
Answer:
The answer is 16.90 because 52.50 minus 35.5 is 16.90.
Which number is rational?
-2.101001001
-.8974512
1.2547569
5.3333333
Answer:
D
Step-by-step explanation:
Took the test
What is the slope and y-intercept? Please help!!
Answer:
y=4x+7
Step-by-step explanation:
a dilation has center (0,0). Find the image of the point L(-4,0) for the scale factor 7.
The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.
To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.
The coordinates of the image point L' will be:
L' = (-4 × 7, 0 × 7) = (-28, 0)
Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
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20. There is a number x sum that x2 is irrational but x is rational. Then x can be
(a) √5102.0 (£)
(b) √2
(c) 3/2
(d) 4/5
The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)
To explain further, we need to understand the properties of rational and irrational numbers.
A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.
In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.
Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.
Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.
Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.
In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)
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graph the inequality x < -4/5
Answer: See the diagram below.
There is an open hole at -4/5 and shading to the left
This visually describes any value that is smaller than -4/5 as stuff to the left is smaller than stuff to the right. The value -4/5 itself is not part of the solution set because we don't have "or equal to" as part of the inequality sign.
Answer:
27
Step-by-step explanation:
the
I need help with this question?
Answer:
Not sure but try
Step-by-step explanation:
1, 6 < 2x
2, c = b2
3, a + g / 5
4, (c^4)7u
5, y > 4(9)
6, e < 10 + p
Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals) a P(z < -1.0)b. P(z 2 -1.0) c. P(z 2 -1.5) d: P(z > -2.5) e P(-3 < 2 < 0)
The probabilities is as follows:
a) P(Z \(\leq\) -1.0) = \(\Phi\)(-1.0) = 0.1587.
b) P(Z \(\geq\) -1.0) = 1 - P(Z < -1.0) = 1 - 0.1587 = 0.8413.
c) P(Z \(\geq\) -1.5) = 1 - P(Z < -1.5) = 1 - \(\Phi\)(-1.5) = 1 - 0.0668 = 0.9332.
d) P(Z \(\geq\) -2.5) = 1 - P(Z < -2.5) = 1 - \(\Phi\)(-2.5)=1-0.0062=0.9938
e) P(-3 < Z \(\leq\) 0) = P(Z \(\leq\) 0) - P(Z < -3) = \(\Phi\)(0) - \(\Phi\)(-3) = 0.5 - 0.0013 = 0.4987.
What is meant by Standard normal distribution?The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1.
Any normal distribution can be made into the conventional normal distribution by converting the ad hoc data into z-scores. Z-scores in a z-distribution show the number of standard deviations that each value deviates from the mean.
Let Z be a random variable following N(0,1).
Then, Z is also called a standard normal variable.
The cumulative distribution function of Z exists represented by Ф(.) where Ф(z) = P(Z \(\leq\) z).
Suppose we wish to find \($P(a \leq X \leq b)$\).
Then, P(a \(\leq\) X \(\leq\) b) = P(X \(\leq\) b) - P(X < a) = \(\Phi(b)-\Phi(a)$\).
Suppose \($Z \sim N(0,1)$\).
a) P(Z \(\leq\) -1.0) = \(\Phi\)(-1.0) = 0.1587.
b) P(Z \(\geq\) -1.0) = 1 - P(Z < -1.0) = 1 - 0.1587 = 0.8413.
c) P(Z \(\geq\) -1.5) = 1 - P(Z < -1.5) = 1 - \(\Phi\)(-1.5) = 1 - 0.0668 = 0.9332.
d) P(Z \(\geq\) -2.5) = 1 - P(Z < -2.5) = 1 - \(\Phi\)(-2.5)=1-0.0062=0.9938
e) P(-3 < Z \(\leq\) 0) = P(Z \(\leq\) 0) - P(Z < -3) = \(\Phi\)(0) - \(\Phi\)(-3) = 0.5 - 0.0013 = 0.4987.
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A rectangle is h units high. It's length 3 units more than it's height. What is the perimeter?
The perimeter of the rectangle is 4h + 6
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, constants and factors.
These expressions are also made up of arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesThe formula for calculating the perimeter of a rectangle is expressed as;
Perimeter = 2( l + h)
Where;
l is the lengthh is the height of the rectanglel = 3 + h
Substitute the values
Perimeter = 2( 3 + h+ h)
expand the bracket
Perimeter = 2(3 + 2h)
Perimeter = 4h + 6
Hence, the expression is 4h + 6
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Abigail is trying to rent a boat while on vacation. She has two options to choose from.
Bruce's Boats: $22.50 per hour plus a one time fee of $85
Peter's Pontoons: $65.00 per hour
After how many hours, will Bruce's Boats, and Peter's Pontoons charge the same amount?
A.130
B.2
C.3
D.85
ANSWER QUICK
Step-by-step explanation:
D bruce's boats: $22.50
Can someone help find the formula for this function.
The formula for this function is y = 0.9 * cos((2π/3) x + π/2) - 1.2
How to derive a cosine functionFrom the image attached, that looks like a cosine graph with 3 periods. 2 highs and 1 low. Also, it should be noted that it is a cosine function.
Therefore to derive the formula for the graph, we use a cosine function with a phase shift and amplitude adjustment.
The general formula for a cosine function is:
f(x) = A * cos(Bx + C) + D
where
A = amplitude,
B = frequency,
C = phase shift,
D = vertical shift.
To get the Amplitude:
We want the function to oscillate between 2.1 and 0.3, which is a difference of 1.8. Since the sine function oscillates between -1 and 1, we need to multiply it by half the desired difference to get the right amplitude. Therefore,
A = 1/2 *1.8 = 0.9.
To get the Frequency:
Since there are only three periods in the interval, then
frequency = 2π/3.
Therefore B = 2π/3.
To get the Phase shift:
We want the function to peak at x = 0, so we need a phase shift of π/2.
Therefore C = π/2.
To get Vertical shift:
We want the function to have a trough at y = 0.3, which means we need to shift it down by 1.8/2 + 0.3 = 1.2. We set D = -1.2.
Putting all these parameters together, we get the following formula:
f(x) = 0.9 * cos((2π/3) x + π/2) - 1.2
This function will oscillate between 2.1 and 0.3 over three periods, with a peak at x = 0 and a trough at y = 0.3.
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Mobiyinion
Reflecting over the x-Axis
Triangle ABC has vertices A(-2, 3), B(0, 3), and C(-1,-1). Find the coordinates of the image after a reflection over
the x-axis.
A
B'
C'
Answer:
A'= (-2,-3)
B'=(0,-3)
C'=(-1,1)
Step-by-step explanation:
coordinates reflected over the x axis follow the rule (x,y) becomes (x,-y). so just multiply each y coordinate by -1 to find the reflected coordinate
Check the picture below.
The equation of a parabola is (x−3)2=16(y+7) . What are the coordinates of the vertex and focus of the parabola? What is the equation of the directrix?
The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.
The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.
Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).
The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).
To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.
In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.
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what will be the answer
1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:
If something weighs more than 2000 pounds, then it weighs more than Jill’s car.
Sally weighs more than 2000 pounds.
Therefore, Sally weighs more than Jill's car.
2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Sally weighs more than Jill's car.
Therefore, Sally is too heavy for the bridge.
What is the Law of Syllogism and the Law of Detachment?The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.
The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.
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6. Solve the equation: h/9 = 7.
A. h = -63
B. h=63
C. h=127
D. h = 7/g
Answer:
B) h=63
Step-by-step explanation:
Multiply both sides by 9.
h/*9=9*7
Simplify
h=63
\(\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }\)
Multiply both sides by 9.
h = 7 × 9Multiply 7 and 9 to get 63.
h = 63 ===> AnswerTherefore, the correct option is "B".
\(\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)
What is the function g(x) that results when translating the function f(x) = |x| to the left 12 units and reflecting it over the x-axis?
Answer: Translation up 5 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+5)g(x)=−(f(x)+5).
-(4x+5)=-4x-5
−(4x+5)=−4x−5
Step-by-step explanation:
Answer:
g(x) = -|x + 12|
Step-by-step explanation:
Translation to left ≡ f(x + 12)
f(x + 12) = | x + 12 |
Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values
Reflected f'(x) = -y = -f(x)
Taken together
g(x) = -(|x + 12|)
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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