The correct equivalent expression is D. [tex]\log_2{256}[/tex].
The given expression is:
[tex]\log_2{16} + \log_2{16}[/tex]
First, we need to simplify the given expression using properties of logarithms.
Using the property:
[tex]\log_b{m} + \log_b{n} = \log_b(m \times n)[/tex]
We can rewrite the given expression as:
[tex]\log_2{16} + \log_2{16} = \log_2{(16 \times 16)} = \log_2{256}[/tex]
Now we can analyze the options given:
A. [tex]\log_2{28}[/tex]: This is not equivalent because 28 is not the same as 256.
B. 8: This is not in logarithmic form and not equivalent to the simplified expression.
C. [tex]\log{256}[/tex]: This is not equivalent because the base here is 10 (common logarithm), while the given expression has a base of 2.
D. [tex]\log_2{256}[/tex]: This is correct because our simplified form is exactly [tex]\log_2{256}[/tex].
Find the lowest common denominator of the following fractions.
A.) 24y2
B.) 24(y2 - 1)
C.) 24(y2 - 1)(y + 1)
Answer:
B.) 24(y² -1)
Step-by-step explanation:
The denominator of the first fraction is 2³(y +1).
The denominator of the second fraction is 2·3(y +1)(y -1).
The LCD is the product of the unique factors to their highest powers:
2³·3·(y +1)(y -1) = 24(y² -1)
Answer:
B
Step-by-step explanation:
A dragonfly traveled a rate of 35 miles per hour for 2.5 hours what distance did the dragonfly travel
Multiply the speed by the time:
35 miles per hour x 2.5 hours = 87.5 miles total.
Answer: 87.5 miles
Step-by-step explanation:
35 miles per 1 hour
35 * 2.5 = 87.5
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle. Can the perimeter of the rectangle be 64 units when its width is 11 units and its length is 20 units?
A.No. If the length is 20 and the width is 11, the perimeter is P = 20 + 22 = 42, not 64.
B.No. If the length is 20 and the width is 11, the perimeter is P = 40 + 22 = 62, not 64.
C.Yes. If the perimeter is 64 units and the width is 11 units, then P + W is greater than D.40.
Yes. If the perimeter is 64 units and the width is 11 units, then P + W is less than 40.
Answer:
B: No
Step-by-step explanation:
P = 2L + 2W. If L = 20 and W = 11, then P = 2(20) + 2(11), or 62. This matches Answer B.
Answer: The correct option is
(B) No. If the length is 20 and the width is 11, the perimeter is P = 40 + 22 = 62, not 64.
Step-by-step explanation: Given that the perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
We are to check whether the perimeter of the rectangle can be 64 units when its width is 11 units and its length is 20 units.
According to the given information, we have
Length, L = 20 units, width, W = 11 units and Perimeter, P = 64 units.
We have
[tex]P\\\\=2L+2W\\\\=2\times20+2\times11\\\\=40+22\\\\=62\neq64.[/tex]
Therefore, if length is 20 units and width is 11 units, then perimeter P = 40 + 22 = 62 units, not 64.
Thus, the answer is NO.
Thus, option (B) is CORRECT.
Which of the following is best modeled using a linear equation y=ax+b, where a is less than 0?
Your answer should be C because the slope line is negative so you're answer should be negative
We are given y = ax + b.
Here, [a] represents the slope.
Which graph shows NEGATIVE SLOPE?
The graph starting at the upper left going to the bottom right is CHOICE C.
CHOICE C is the answer because the slope [a] must be negative.
What is the inter-quartile range of the given data set?
2
3
6
Answer:
Inter-quartile range = 3 .
Step-by-step explanation:
Given : diagram with data.
To find : What is the inter-quartile range of the given data set.
Solution : We have given data .
We can see from the given data lowest value of data is 15 .
highest value of data = 21.
First quartile ( Q1) = 17
Second quartile (Q2) =18
Third quartile (Q3) = 20.
Inter-quartile range = Third quartile (Q3) - First quartile ( Q1) .
Inter-quartile range = 20 - 17
Inter-quartile range = 3 .
Therefore, Inter-quartile range = 3 .
Help with this question, please!
Answer:
The last choice is the one you want.
Step-by-step explanation:
Simply take the x coordinate and subtract 4, then do the same with the y coordinate since the vector movement is <-4, -4>. The first coordinate F is <4,0>. Subtract 4 from both of those coordinates and end up at <0, -4>. The second coordinate G is <1, 3>. Subtract 4 from both of those and end up at <-3, -1>. The third coordinate H is <2, 6>. Subtract 4 from both of those and end up at <-2, 2>. The last coordinate I is <4, 2>. Subtract 4 from both of those and end up at <0, -2>.
Type the correct answer in each box. The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches
Answer:
5 is the width and 7 is the length
Answer:
x=5 in (Width)
x+2=5+2=7 in (Length)
Step-by-step explanation:
You are given the equation 2x+2(x+2)=24 to solve for x where x is the width.
First step, use distributive property 2x+2x+4=24
Second step, subtract 4 on both sides and combine the like terms on the left hand side: 4x=20
Divide both sides by 4: x=20/4
So x=5 in
And since length is 2 more than the width so the length is 2+5=7 in
If an unfair coin is tossed into the air and drops without interruption, its probability of landing on heads is 0.51 whereas the probability of landing on tails is 0.49. If the payoff for landing on heads is $0.99 and the payoff for landing on tails is $1.01 and it costs $1 to play each game, should you play?
1)Yes, because over the long run your expected value is greater than the lowest payoff
2)No, because over the long run your expected value is lower than the lowest payoff
3)Yes, because over the long run your expected value is greater than the cost to play
4)No, because over the long run your expected value is less than the cost to play
Answer:
4) No, because over the long run your expected value is less than the cost to play
Step-by-step explanation:
The expected value is ...
0.51×0.99 + 0.49×1.01 = 0.5049 +0.4949 = 0.9998
This expected value is less than the cost to play, so you will lose money in the long run. You should not play.
Identify the transformation that appears to be a reflection. HELP ASAP!!
Answer: the first option
Step-by-step explanation:
A reflection means that the object is flipped.
A reflection is a transformation that flips a shape over a line, creating a mirror image. You identify a reflection by looking for a shape which appears to have been flipped across a line.
Explanation:In mathematics, a reflection is a type of transformation that flips a shape over a line, creating a mirror image. To identify a reflection, you should look for a shape that appears to be flipped over a line. This line is called the line of reflection. For example, if you have a triangle ABC and its image A'B'C' such that A'B'C' is a mirror image of ABC, this is a reflection. The point A is reflected over the line to point A', B to B', and C to C'. The distances from the line of reflection to A, B, and C are equal to the distances from the line to A', B', and C' respectively.
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Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. He currently charges in half-hour intervals. Recall the inequality that represents this situation: . Ezra decides to charge per dog instead of per hour. How does the solution set change? What are the limitations on x and y? Explain.
Answer:
The limitations on y-values changed from non-negative multiples of one-half to whole numbers, since Ezra cannot walk a fractional number of dogs.
The limitations on x-values did not change and must be non-negative multiples of one-half, since Ezra cannot work negative hours and charges by the half-hour.
The inequality x + y >= 1100 represents Ezra's earnings from his two jobs. If he changes his dog-walking fee to a per dog amount, the inequality changes to x + z >= 1100, shifting the solution set. This impacts the number of lawn mowing and dog walking jobs Ezra must do to earn at least $1100.
Explanation:The question involves understanding of inequalities and how the solution set changes when the conditions change. Suppose Ezra earns x dollars for every lawnmowing job and y dollars for every dog-walking job. Then, his earnings would be represented by the inequality: x + y >= 1100.
Now, if he changes his dog-walking charges to be per dog instead of per hour, say z dollars per dog, we can modify our inequality to: x + z >= 1100.
The solution set for the new inequality would include all values of x and z that makes the inequality true - essentially how many lawn mowing and dogs walking jobs he needs to do to earn at least $1100. One thing to bear in mind is that both x and z must hold positive value since one cannot earn negative money from a job.
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PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
-5
Step-by-step explanation:
∛-25 × ∛5
= ∛-75
= ∛(-5)^3
= - 5
Answer:
a
Step-by-step explanation:
(-25)^⅓ × 5^⅓
(-25 × 5)^⅓
(-125)^⅓
(-5)³^⅓
-5
Could someone possibly explain to me how to find the probabilities for a binomial random variable? I think just explaining one could guide me into answering all of them.
n=10 and p=.6
P(x ≤ 8)
Answer:
n is the fixed number of trials. x is the specified number of sucesses. N - X is the number of failures. P is the probablity of success on any given trail. 1 - P is the probabilty of failure on any given trial.
These probabilities hold for any value of X between 0 (lowest number of possible successes in n trials) and n (highest number of possible successes).
Hope this helps
Step-by-step explanation:
Need help with a math question
Answer:
72%
Step-by-step explanation:
You are looking at graduate students. There are 2610 of them.
Of those graduates 1879 have financial aid.
So the probability of a graduate student having financial aid is 1879/2610.
Inserting this division into my calculator provides me with about 72%.
Need help with this math question
Answer:
-12 is the correct answer
Answer:
The equation for the circle is (x-0)^2+(y+3)^2=25
Step-by-step explanation:
The radius is half the diameter. To find the length of the diameter we need to calculate the distance that (3,1) is to (-3,-7) which is sqrt(6^2+8^2)=10 .
The radius is therefore 10/2=5.
We also need the center of the circle (the midpoint of a diameter is the center of a circle). So we just need to average the x's and y's to find the midpoint between (3,1) and (-3,-7) which is (0,-3).
The equation for the circle is (x-0)^2+(y+3)^2=25
I just plugged my info into (x-h)^2+(y-k)^2=r^2
where (h,k) is center and r is radius
{8x + 9y = −3 6x + 7y = 1 What values of x and y satisfy the system of equations
Answer:
A) 8x + 9y = −3
B) 6x + 7y = 1
We multiply A) by -(6/8)
A) -6x -6.75y = 2.25 then we add this to equation B
B) 6x + 7y = 1
.25y = 3.25
y = 13
and x = -15
Step-by-step explanation:
The value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3 and 6x+7y=1.
Let’s solve the system of equations:
8x+9y=−3
6x+7y=1
We can solve the system of equations using elimination.
Steps to solve:
1. Solve the second equation for y:
y= 1/7
2. Substitute this value of y into the first equation:
8x+9(1/7)=−3
8x+9/7 =−3
8x=−120
x=−15
3. Substitute x=-15 back into the second equation to solve for y:
6(−15)+7y=1
−90+7y=1
7y=91
y=13
Therefore, the value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3 and 6x+7y=1.
given the function y= 5x - 3, complete the table of values by entering the missing value.
x | -3 | -1 | 0 | 2 |
____________
y |-18 | -8 | -3 | |
Answer:
missing value: 7
Step-by-step explanation:
Put 2 where x is in the function and do the arithmetic.
y = 5·2 -3 = 10 -3 = 7
The value corresponding to x=2 is y=7.
To complete the table of values for the function y = 5x - 3, you substitute the given x-value into the equation. The missing y-value for x=2 is 7.
Explanation:The function provided is y = 5x - 3. This is a linear function. To get the y values, you need to substitute the x values from the table into this equation. For the last row where x = 2, substitute 2 into the equation:
y = 5(2) - 3 = 10 - 3 = 7
So, the y-value corresponding to x=2 is 7.
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Match the following linear function to the corresponding graph
Answer:
a red graph
Step-by-step explanation:
slope is 5 and the y intercept is negative 2(the y intercept is where the line crosses the y axis) then you rise over run
3. The sides of an angle inscribed in a circle are
A. a diameter and a tangent.
B. a tangent and a radius.
C. two chords.
D. two radii.
Answer:
C. two chords
Step-by-step explanation:
If the sides of an angle are inscribed in a circle that means that the endpoints of the sides of said angle lie on the circle. That makes both of them chords.
A diameter has to go through the center
A tangent is outside the circle
A radius comes from the center of the circle and meets the outside of the circle
The sides of an angle inscribed in a circle are two radii. These two radii connect from a single point on the circumference of the circle to two different points on the circumference.
Explanation:In the field of Geometry, particularly in relation to circles, the sides of an angle that is inscribed in a circle constitute two radii. An inscribed angle is an angle formed by two lines (in this case, two radii) drawn from a single point on the circumference of a circle to two different points on the circumference. Therefore, the correct answer to the given problem would be option D, which states that the sides of an inscribed angle in a circle are two radii.
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Did I set this problem up correctly and/or how do I solve it? (Angles of polygons)
[tex]\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n=sides'~number\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =140 \end{cases}\implies n140=180(n-2) \\\\\\ 140n=180n-360\implies 140n+360=180n\implies 360=40n \\\\\\ \cfrac{360}{40}=n\implies 9=n[/tex]
A rancher wants to fence in an area of 1,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. Find a function that models the amount of fencing in terms of the width of the field, w, where w is the measurement of the fence down the middle of the field.
Answer:
f(w) = 3w + 2,000,000/w
Step-by-step explanation:
We know that the area of a rectangle is the product of its length and width:
A = LW
Filling in the given values lets us write an expression for the length of the field.
1,000,000 = Lw
L = 1,000,000/w
Since there are 3 fences of length w and two of length L, the total perimeter fence length is the sum ...
f(w) = 3w + 2(1,000,000)/w
Combining the constants, we have a function for the perimeter fence length in terms of the width of the field:
f(w) = 3w +2,000,000/w
Final answer:
The function that models the amount of fencing required for a 1,000,000 square foot rectangular field divided in half by a fence is F(w) = 3w + 2,000,000 / w. This represents the total length of fencing as a function of the width w.
Explanation:
The student is asking for a function that models the amount of fencing required for a rectangular field with an area of 1,000,000 square feet, which is then divided in half by a fence parallel to the width, w. To begin, let's denote the length of the field as L and the width as w. Since the area of the rectangle is given by L multiplied by w, and we know that the area is 1,000,000 square feet, we can express the length L in terms of w as L = 1,000,000 / w.
Now, total fencing required would be the perimeter of the rectangle plus the additional fence dividing it in half. The perimeter is calculated as 2w + 2L. Therefore, the total fencing F in feet would be F(w) = 2w + 2L + w.
Substituting L with 1,000,000 / w, the function becomes F(w) = 2w + 2(1,000,000 / w) + w = 3w + 2,000,000 / w. This function represents the total length of fencing needed in terms of the width w of the field.
What is the equation of the ellipse with vertices at (-25, 0), (25, 0) and co-vertices (0, -15), (0, 15)?
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=25\\ b=15 \end{cases}\implies \cfrac{(x-0)^2}{25^2}+\cfrac{(y-0)^2}{15^2}=1\implies \cfrac{x^2}{625}+\cfrac{y^2}{225}=1[/tex]
Given the following linear functions determine the relationship
Answer: perpendicular
Step-by-step explanation:
Lines with opposite and negated slopes are perpendicular, you can use desmos to graph and check
Answer:
perpendicularStep-by-step explanation:
The product of the slopes (5/6), (-6/5) is -1, so the lines described by these functions are perpendicular.
In the diagram shown, /Il m, m
1 = 3x + 25 and m_8 = 4x - 17.
Find the measure of 2.
29
49°
131°
151
Answer:
29°
Step-by-step explanation:
Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.
m∠1 = m∠8
3x+25 = 4x-17
42 = m . . . . . . . . add 17-3x
Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...
m∠2 = 180° -151° = 29°
What solid is generated when the semicircle is rotated about the line?
A. sphere
B. cone
C. solid cylinder
D. hollow cylinder
Answer:
If the semicircle rotated around the line, it would become a sphere. So, A. sphere.
Step-by-step explanation:
A sphere is generated when a semicircle is rotated about the line.
What is solid revolution?A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line.
What is sphere?Sphere is the set of all points in three-dimensional space lying the same distance from a given point or the result of rotating a semicircle about one of its diameters.
According to the given question.
A semicircle is rotated about the line.
Now,
From the definition of sphere we can say that, when a semicircle is rotated about a line a sphere will generate.
Therefore, a sphere is generated when a semicircle is rotated about the line.
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Please help me solve the problem
Answer:
1
Step-by-step explanation:
When you take the log of ...
b = b^1
you get ...
[tex]\log_{b}{b}=1[/tex]
(Pls help) I need help finding x!
Answer:
x ≈ 46°
Step-by-step explanation:
Since the triangle is right use the sine ratio to solve for x
sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{14}[/tex], hence
x = [tex]sin^{-1}[/tex] ( [tex]\frac{10}{14}[/tex] ) ≈ 46°
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
A.V=[tex]\frac{2}{3}\\[/tex](pi)(r²)
B.V=[tex]\frac{4}{3}\\[/tex](pi)(r³)
C.V=[tex]\frac{1}{3}\\[/tex](pi)(r³)
D.V=[tex]\frac{1}{3}\\[/tex](pi)(r²)
Answer:
B
Step-by-step explanation:
Assume the radius is r so the diameter is 2r
Height=2*d=2(2r)=4r since the diameter is twice the radius
Volume of cone=1/3 * pi*r^2*h
= 1/3 * pi*r^2*(4r)
=4/3 *pi *r^3
So B
Answer: B
h=2d
r=d/2
so h in terms of r is;
h=4r
V=pi*r^2*h/3
V=pi*r^2*4r/3=pi*4r^3/3=4/3(pi)(r^3)
A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use (pie=3.14).
Answer:
radius = 30 ydcost of cement = $7065Step-by-step explanation:
First we find the area of the circular sectors. From that we can find the cost of cement and their radius.
The area of the playground is ...
playground area = (109 yd)^2 = 11,881 yd^2
Then the area of the skating rinks is ...
rink area = playground area - remaining field
rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2
Then the cost of cement for the rink area is ...
(2826 yd^2)($2.50/yd^2) = $7065
__
The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...
A = πr^2
Substituting what we know, we have ...
2826 = 3.14r^2
900 = r^2 . . . . . . . . divide by 3.14
30 = r . . . . . . . . . . . take the square root
The radius of each quadrant is 30 yards.
Which equation represents the partial sum of the geometric series?
For this case we expand the series for each value of "n":
[tex]125 (\frac {1} {5}) ^ {1-1} +125 (\frac {1} {5}) ^ {2-1} +125 (\frac {1} {5}) ^ {3 -1} +125 (\frac {1} {5}) ^ {4-1} =[/tex]
[tex]125+ \frac {125} {5 ^ 1} + \frac {125} {5 ^ 2} + \frac {125} {5 ^ 3} =\\125+ \frac {125} {5} + \frac {125} {25} + \frac {125} {125} =\\125 + 25 + 5 + 1[/tex]
So, the correct option is: A
Answer:
Option A
Answer:
It’s A
Step-by-step explanation:
A city is adding a brick border around the community garden. The garden has the dimensions of x ft by x ft. The dimension of the brick border are x + 12 ft by x + 12 ft. What is the area of the brick border
Answer:
The area of the brick border is [tex](24x+144)\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of the brick border is equal to
[tex]A=(x+12)(x+12)-(x)(x)\\ \\A=(x+12)^{2} -x^{2}\\ \\A=x^{2}+24x+144-x^{2}\\ \\A=(24x+144)\ ft^{2}[/tex]