Answer:
He used the wrong expression to represent the area of the base of the pyramid.
Step-by-step explanation:
i just took it yesterday
Vikram made an error in the expression to represent the area of the base of the pyramid. So, Option B is correct.
What is the surface area of a square pyramid?The surface area of a square pyramid is given by the formula,
[tex]SA=s^2+4(\frac{1}{2}bh)[/tex]
Where, s-length of the side of the square, b- length of the base,
and h- the height of the pyramid.
Given data:The square base had a side of length s=34.2 inches
The height h=28.4 inches
Calculating the surface area:The surface area is given by the expression:
[tex]SA=s^2+4(\frac{1}{2}bh)[/tex]
On substituting the values
[tex]SA=(34.2)^2+4(\frac{1}{2}(34.2)(28.4))[/tex]
But Vikram wrote,
[tex]SA=(33.2)(34.2)+4(\frac{1}{2}(34.2)(28.4))[/tex]
So, he used the wrong expression for the area of the base of the pyramid.
Therefore, option B is correct.
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a hotel swimming pool is made up of four semicircles and a square. Find the perimeter of the swimming pool. Round your answer to the nearest tenth
Answer:
62.8
Step-by-step explanation:
d=10
10x3.14
31.4
31.4x2
62.8 is the perimeter
The coroner arrives at the scene of a murder at 11 p.m. She takes the temperature of the body and finds it to be 81.7°F. She waits 1 hour, takes the temperature again, and finds it to be 80.2°F. She notes that the room temperature is 67°F. When was the murder committed?
Answer:
11:45 AM
Step-by-step explanation:
We have that in one hour the body temperature decreased
went down in
81.7 - 80.2 = 1.2
i.e. 1.2 degrees.
Normal body temperature is 98.6 degrees.
The difference between normal and 11 pm is 98.6-81.7 = 16.9
i.e. 16.9 degrees
now to know how much it decreases every hour:
16.9/ 1.5 = 11.26, that is 11 hours and 15 minutes (1/4 of an hour)
If that was 11:00 PM - 11:15 minutes, the murder was at 11:45 AM
Final answer:
To determine the time of death using body temperature changes from normal to discovered levels, applying physics principles is essential.
Explanation:
The time of death for the old man can be determined by calculating the rate at which body temperature decreases from the normal level to the discovered level. In this case, we have a normal body temperature of 37°C, a discovered temperature of 28°C, and subsequent temperatures of 24°C and 0°C. Using the information provided, the time of death for the old man was approximately 10:00 PM.
This calculation is based on the rate of body temperature decrease from the point of discovery to the hospital, considering the normal body temperature, room temperature, and the temperatures recorded during the investigation. This scenario demonstrates the application of physics principles in forensic investigations to determine the time of death based on body temperature changes.
A shoe store is selling a pair of shoes for $60 that has been discounted by
25%. What was the original selling price?
Answer:
$80
Step-by-step explanation:
25% is 1/4 of a whole with 75% of the cost left over, so $60 is 1/3 of the price. divide 60 by 3=$20, $20 discounted, original price $80
Two angles of a quadrilateral measure 25° and 280°. The other two angles are in a ratio of 5:6. What are the measures of those two angles?
Answer:
25 and 30
Step-by-step explanation:
because one angle measures 280 and the other 25 you add it.
280 + 25 = 305
Since there is 360 degrees in a quadrilateral you subtract
360 - 305 = 55
the other 2 measures are in the ratio of 5:6
So add those to ratios 5 + 6 = 11
55/11 = 5
multiply it by the ratio
5 * 5 = 25
5 * 6 = 30
17 Points! Help Me please!
Answer:
This is the completed table:[tex]\left[\begin{array}{ccccccccccc}trapezoids&1&2&3&4&5&6&10&18&n\\perimeter&10&16&22&28&34&40&64&112&6n+4\end{array}\right][/tex]
for the words and graph please see below and the attached image.
Step-by-step explanation:
Notice that every time you add a trapezoid in the given fashion (attached to the right of the previous figure) yo are adding a net of 6 units (2+4) to the total perimeter (which started in the first figure as 2+2+2+4 = 10).
We can then write the following values to complete the given table:
1 trapezoid , gives perimeter = 1*4 + 3*2 = 10
2 trapezoids, give perimeter = 2*4 + 4*2 = 16
3 trapezoids, give perimeter = 3*4 + 5*2 = 22
4 trapezoids, give perimeter = 4*4 + 6*2 = 28
5 trapezoids, give perimeter = 5*4 + 7*2 = 34
6 trapezoids, give perimeter = 6*4 + 8*2 = 40
10 trapezoids, give perimeter = 10*4 + 12*2 = 64
n trapezoids, give perimeter = n*4 + (n+2)*2 = 4n + 2n + 4 = 6n + 4
Now, given this general relationship for "n" trapezoids, one can find the number of trapezoids that render a perimeter = 112, as required in the table:
6n + 4 = 112
then 6n = 112 - 4 = 108
then n= 108/6 = 18
so 18 trapezoids give a perimeter of 112 (to complete that missing value in the table).
Now, we can plot a general function of similar form of that we got for a collection of n trapezoids but using "x" instead of "n" and having clear in our mind that the values we want to use are only positive integers greater than zero to represent the number of trapezoids:
f(x) = 6x +4
See attached image were the actual valid points are marked as blue dots.
A sphere has a radius of 5 inches. What is its volume?
Sphere V =
np3
1. Substitute the radius into the formula:
2. Evaluate the power:
V = 4(53)
V = T(125)
V = 125
3.
Simplify:
in.
The volume of a sphere with a radius of 5 inches is 523.6 cubic inches.
Explanation:To find the volume of a sphere, you can use the formula V = (4/3)πr³, where V represents the volume and r represents the radius.
In this case, the radius is given as 5 inches. So we substitute 5 into the formula:
V = (4/3)π(5)³
Simplifying the expression:
V = (4/3)π(125)
Finally, we calculate the volume:
V = 523.6 cubic inches
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Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?
(negative 8, infinity)
(8, infinity)
(negative infinity, 8)
(negative infinity, negative 8)
Answer:
A. -8, infinity
Step-by-step explanation:
2020 edg
Using quadratic function concepts, it is found that the function is decreasing over the interval (-8, infinity).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient, determining the behavior of the function as follows.
If a > 0, it decreases for (-infinity, h) and increases for (h, infinity).If a < 0, it increases for (-infinity, h) and decreases for (h, infinity).In this problem, the equation is given by:
[tex]f(x) = -(x + 8)^2 - 1[/tex]
Hence the coefficients are a = -1 < 0, h = -8, k = 1, meaning that the function is decreasing over the interval (-8, infinity).
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What is the lcm of 8,12,3
Answer: 24
Step-by-step explanation:
Lowest common multiple means the lowest number that can be divisible by 8,12,3
Looking at this, let's pick 8&3 first
8×3=24
12×3=36
12×8=96
Looking at this value,24 seems to be the lowest,
Therefore the lowest common multiple is 24
2000 is placed into a bank account that pays 3% compound interest per year
The compound interest on 2000 is 60.
Step-by-step explanation:
Given,
Principal (P) = 2000
Rate of interest (r) = 3%
Time (T) = 1 years
To find the interest calculated compound in 1 year.
Formula
Amount = P[tex](1+\frac{r}{100} )^{T}[/tex]
Putting the given values we get,
Amount = 2000[tex](1+\frac{3}{100} )^{1}[/tex]
= 2060
So,
The interest = 2060-2000 = 60
A sidewalk around a circular garden is 3 feet wide what is the area of the sidewalk
We can see here that the area of the sidewalk surrounding the circular garden is approximately 216.66 ft².
To find the area of the sidewalk surrounding the circular garden, we need to calculate the difference between the area of the larger circle and the area of the smaller circle.
The radius of the circular garden is given as 10 ft. The radius of the garden plus the sidewalk is equal to the sum of the radius of the garden and the width of the sidewalk. Since the width of the sidewalk is 3 ft, the radius of the larger circle (including the sidewalk) is 10 + 3 = 13 ft.
Now, let's calculate the area of the larger circle using the formula A = πr², where A represents the area and r represents the radius. Substituting the values, we have A = 3.14 × (13)² = 3.14 × 169 = 530.66 sq ft.
Next, we calculate the area of the smaller circle (just the garden) using the same formula. A = 3.14 × (10)² = 3.14 × 100 = 314 sq ft.
Finally, we subtract the area of the smaller circle from the area of the larger circle to find the area of the sidewalk. 530.66 - 314 = 216.66 sq ft.
Therefore, the area of the sidewalk surrounding the circular garden is approximately 216.66 square feet.
The complete question is:
A sidewalk that is 3 ft wide surrounds a circular garden with a radius of 10 ft. What is the area of the side walk? use pi=3.14
On Tuesday, Franklin deposited $35 into his account. On Wednesday, he withdrew $25. Evaluate the expression ⎪35⎥ - ⎪-25⎥ to find the net change of his account.
Question 7 options:
A:10
B:-10
C:None of the Above
D:60
The net change of Franklin's account is 10.
Explanation:Subtraction is a fundamental arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-). To subtract one number from another, align the digits according to place value and subtract each column, starting from the rightmost column
To find the net change of Franklin's account, we need to evaluate the expression |35| - |-25|.
The absolute value of 35 is 35, and the absolute value of -25 is 25.
Subtracting these values, we have 35 - 25 = 10.
Therefore, the net change of Franklin's account is 10.
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please help
Jonathan is trying to drain his pool to install a new liner. The graph below represents the amount of water remaining in his pool as he drains it.
A)
Number of Gallons drained per hour; Number of hours (Independent Variables)
Number of Gallons in the pool (Dependent Variable)
B) -25 (It's the negative value of how many gallons are drained in an hour)
C)13000 (It means how many gallons were in the pool to begin with)
D)3000 (It's the corresponding value for 40 as the x-value)
Michael recorded the color of each car that passed by his office. He saw 30 blue cars and 40 green cars. What is the experimental probability that the next car Michael sees will be a blue car?
Answer:
3/7
Step-by-step explanation:
The two sets of data below show the number of bubbles blown in fifty trials using two different bubble solutions.
A box plot titled Bubbles Created with Solution 1. The number line goes from 80 to 116. The whiskers range from 80 to 114, and the box ranges from 100 to 112. A line divides the box at 110.
Bubbles Created with Solution 1
A box plot titled Bubbles Created with Solution 2. The number line goes from 72 to 110. The whiskers range from 72 to 110, and the box ranges from 74 to 80. A line divides the box at 76.
Bubbles Created with Solution 2
Which best describes the measure of center that can be used to most accurately compare the two data sets?
the mean, because it increases the influence of outliers
Answer:
d
Step-by-step explanation:
i got it right
Answer:
the median, because it decreases the influence of outliers
Step-by-step explanation:
Logan rode his bike 2 1/2 miles in 10 minutes. At this pace, how far can Logan ride his bike in an hour?
a.4 miles
b.25 miles
c.15 miles
d.10 miles
The principal of Brookefield Middle School maintains order by appointing 2 hall monitors for every corridor, and 4 teachers for every 12 hall monitors. If the school has 24 corridors, how many teachers would be required to maintain order in the school?
a.16
b.14
c.12
d.18
The expression 96.8 + (365.21 - 98.76) represents A.
The expression 96.8 + (64.87 - 71.25) represents B.
The numerical value of A - B is)_______
The numerical value of B - A is)_______
Maura works at a car dealership. She earns a base salary plus a commission that is 7% of her total sales.
How much commission does Maura earn from a $30,000 sale?
a.2,100
b.210
c.4,286
d.9,00
Answer:
The first one is c.
The second one is a.
third is 272.83 and -272.83
fourth is a
Step-by-step explanation:
your welcome
Solve this question
Answer:
∠ RQU = 25°
Step-by-step explanation:
The opposite angles of an inscribed circle are supplementary, thus
∠ URS + ∠ UTS = 180°, that is
∠ URS + 124° = 180° ( subtract 124° from both sides )
∠ URS = 56°
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ URS is an external angle to Δ QUR, that is
∠ RQU + 31° = 56° ( subtract 31° from both sides )
∠ RQU = 25°
What aspect of this graph is likely being emphasized by the choice of graph style, choice of scale, and so on? a. the unrelated nature of the data b. the broad differences over short intervals c. the total values of the data as a whole d. the indirect connection between weight and leaf content
Answer:
D
Step-by-step explanation:
Answer is D.
Answer:
d.
the indirect connection between weight and leaf content
Step-by-step explanation:
The 8 students in Mrs. Clark's dass were asked how many minutes it takes them to get to school in the morning. Here is what they answered:
13, 4, 8, 15, 15, 11, 16,3
Find the mean and median travel times for these students.
If necessary, round your answers to the nearest tenth.
Answer:
mean=10.625=10.6
median=12
Step-by-step explanation:
Mean
The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, what is meant by the "mean" changes. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values. The equation for calculating an arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used
Median
The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers. Note that when calculating the median of a finite list of numbers, the order of the data samples is important. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results. In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values. While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample. In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same
plz mark brainliest
I need help I don’t really don’t understand this and the first on I will give you brainlist
What is the answer 2+495758?
Answer:
495760
Step-by-step explanation:
Answer:
495760
Step-by-step explanation:
add 2 to 8
Q12: Annette plans to visit an amusement park where she must pay for admission and purchase tickets to go on the rides. Annette wants to find the total cost for a day at the amusement park. She wrote the equation c=1.50x+12 to predict c, the total cost for a day at the amusement park. What could the number 12 represent in Annette’s equation? A the number of rides B the cost of admission C the cost of each ticket D the number of tickets
Answer:
B
Step-by-step explanation:
B because an admission is a constant.
Answer:
C=1.50x+12
Step-by-step explanation:
1 ride with admission is $13.50
2 rides with admission is $15.00
3 rides with admission is $16.50
4 rides with admission is $18.00
It's $1.50(x) difference between each total cost(c) letting us know that is the cost for 1 ticket meaning it cost $12.00 for admission.
2n - 5 = 31
Answer: The value of n is ....
Answer:
n = 18
Step-by-step explanation:
2n - 5 = 31
Add 5 to each side
2n - 5+5 = 31+5
2n = 36
Divide each side by 2
2n/2 = 36/2
n = 18
The circumference of a circle is 16π cm. What is the area, in square centimeters? Express your answer in terms of \piπ.
Answer:
64 pi
Step-by-step explanation:
lmk if you need an explanation
Answer:
[tex]64\pi[/tex]
Step-by-step explanation:
The area of a circle can be found using:
[tex]a=\pi r^{2}[/tex]
We have the circumference, but we need the radius. Circumference can be found using:
[tex]c=2\pi r[/tex]
We know the circumference is 16[tex]\pi[/tex], so we can substitute that in for c
16[tex]\pi[/tex] =2[tex]\pi[/tex] r
We need to solve for r, or the radius. To do this, divide both sides by 2[tex]\pi[/tex]. This will get r by itself.
16[tex]\pi[/tex] /2[tex]\pi[/tex] =2[tex]\pi[/tex] r/2[tex]\pi[/tex]
8=r
Now we know the radius, and can substitute it into the area formula
[tex]a=\pi r^2[/tex]
Substitute 8 in for r
[tex]a=\pi 8^2[/tex]
[tex]a=64\pi[/tex]
This answer is expressed in terms of pi, since it includes pi in the answer. Therefore, the area, in terms of pi is [tex]64\pi[/tex]
idk what I should do
Answer:
c.
Step-by-step explanation:
All of the things are correct with this one.
Find A U C.
A) {2,3,5,6,7,9,11}
B) {3,5,6,7,8,11,12}
C) {3,5,6,7}
D) {3,5,7}
Answer:
A U C = {2,3,5,6,7,9,11}
Step-by-step explanation:
A = {2,3,5,6,7,9,11}
C = {3,5,6,7}
The union of two sets is a set that has every element that belongs to one or the other set.
A U C = {2,3,5,6,7,9,11}
What’s the value??????
Answer:
x = -1, x = 3 (B)
Step-by-step explanation:
25ˣ=5ˣ²⁻³
Can be simplified to:
5²ˣ=5ˣ²⁻³
2x=x²-3
x²-2x-3=0
(x-3)(x+1)
x = -1, x = 3
Plz mark my answer as brainiest
Answer:
B x=-1 x=3
Step-by-step explanation:
25^x = 5 ^ (x^2 -3)
Replace 25 by 5^2
5^2^x = 5 ^ (x^2 -3)
We know that a^b^c = =a^(b*c)
5^(2x) = 5 ^ (x^2 -3)
The bases are the same so the exponents must be the same
2x = x^2 -3
Subtract 2x from each side
2x-2x = x^2 -3 -2x
0 = x^2 -2x-3
Factor
0 =(x-3) (x+1)
Using the zero product property
x-3 =0 x+1 =0
x=3 x=-1
To make f continuous at x=2 , f(2) should be defined as what value? Justify your answer.
Answer:
To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]
Step-by-step explanation:
A function, let say [tex]f(x)[/tex], is defined at [tex]x = c[/tex] is continuous at [tex]x = c[/tex]
If the limit of [tex]f(x)[/tex] as [tex]x[/tex] approaches [tex]c[/tex] is equal to the value of [tex]f(x)[/tex] at [tex]x = c[/tex].
Mathematically it is written as:
if
[tex]\lim _{x\to c}\:f\left(x\right)=f\left(c\right)[/tex]
then
[tex]f(x)[/tex] is continuous at [tex]x = c[/tex].
So from the above definition, we conclude that:
To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]
i.e.
if
[tex]\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)[/tex]
then
[tex]f(x)[/tex] is continuous at [tex]x = 2[/tex].
To make f continuous at x=2, define f(2) to be equal to 4. This makes the left-hand limit, right-hand limit, and function value at x=2 all equal to 4, which satisfies the definition of continuity.
To make a function continuous at a point, the left-hand limit and right-hand limit at that point must be equal to the function's value at that point. In other words, if a function is continuous at x=a, then
[tex]\lim_{x \to a^+} f(x)=f(a)[/tex]
Therefore, to make f continuous at x=2, we must define f(2) to be equal to the limit of f(x) as x approaches 2 from both the left and the right.
We can see that the limit of f(x) as x approaches 2 from the left is 4. This is because f(x) approaches 4 as x approaches 2 from the left, even though f(2) is undefined.
We can also see that the limit of f(x) as x approaches 2 from the right is 4. This is because f(x) approaches 4 as x approaches 2 from the right, even though f(2) is undefined.
Therefore, to make f continuous at x=2, we must define f(2) to be equal to 4.
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Please Help! If (5x-2)^2=ax^2-bx+c, what is the value of a+c^2?
Answer:
The solved problem is in the photo. Hope it helps.
The value of a, b, and c is 25, -20, and 4 respectively. Then the value of the expression will be 41.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
If (5x - 2)² = ax² - bx + c.
Then the value of the expression will be a + c²
Open the bracket, then we have
(5x - 2)² = 25x² - 20x + 4
Then the value of the a, b, and c will be
a = 25, b = -20, c = 4
Then the value of the expression a + c² will be
→ 25 +4²
→ 41
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50 pts !!! What is the product of x+2 and x-7? Write your answer in standard form.
Please use the foil method. show all work!!!
Answer:
x^2-7x+2x-14 or x squared minus seven x plus two x minus fourteen
Step-by-step explanation:
(x+2)*(x-7)= x^2-7x+2x-14
First: x^2
Outer: -7x
Inner: 2x
Last: -14
Answer:
x²-5x-14
Step-by-step explanation:
Write the equation (x+2)(x-7)
Multiply (F in FOIL)
x*x =x²
Multiply (O in FOIL)
x*-7 = -7x
Multiply (I in FOIL)
2*x = 2x
Multiply (L In FOIL)
2*-7 = -14
Combine like terms
-7x + 2x = -5x
Write the equation
x²-5x-14
The area of a rhombus can be evaluated using the formula 1/2d1d2 where d1 represents the measure of one of its diagonals and d2 represents the measure of its other diagonal. When d1 is a terminating decimal and d2 is a repeating decimal, what can be concluded about the area of the rhombus?
The area of the rhombus is a rational number, specifically 5/12, which can be expressed as a fraction. Therefore, we can conclude that when d1 is a terminating decimal and d2 is a repeating decimal, the area of the rhombus can be expressed as a rational number.
What are the rational numbers?
When d1 is a terminating decimal and d2 is a repeating decimal, we can conclude that the area of the rhombus can be expressed as a rational number.
To see why, consider the formula for the area of a rhombus: A = (1/2)d1d2. If d1 is a terminating decimal, it can be expressed as a finite fraction.
For example, if d1 = 1.25, then d1 can be expressed as 5/4. If d2 is a repeating decimal, it can be expressed as an infinite series of the form:
d2 = a + b/10 + c/100 + ...
where a, b, c, etc. are digits. We can express this as a fraction by multiplying both sides by a power of 10 which eliminates the repeating decimal. For example, if d2 = 0.666..., we can multiply both sides by 100 to get:
100d2 = 66.666...
Subtracting d2 from both sides, we get:
99d2 = 66
So, d2 = 66/99, which can be simplified to 2/3.
Substituting these values into the formula for the area of the rhombus, we get:
[tex]A = (1/2)(5/4)(2/3)\\= 5/12[/tex]
So, the area of the rhombus is a rational number, specifically 5/12, which can be expressed as a fraction. Therefore, we can conclude that when d1 is a terminating decimal and d2 is a repeating decimal, the area of the rhombus can be expressed as a rational number.
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