Answer:
A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.
making it a 33% chance of one of the toddler triplets to end up with their own coat.
100% divided by 3 = 0.33
Please help me with this question.
The constants A and B for the differential equation are given as follows:
A = 0.B = -64.How to obtain the constants A and B?The solutions to the differential equation are given as follows:
y(t) = e^(8t).y(t) = e^(-8t).This means that the roots of the characteristic equation are given as follows:
r = -8 and r = 8.
Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:
(r + 8)(r - 8) = r² - 64.
Hence the differential equation is given as follows:
y'' - 64y = 0.
Hence the constants are given as follows:
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During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function
The daily cost to heat a building at 10 degrees celsius is $82.72
How to interpret the function valuesFrom the question, we have the following parameters that can be used in our computation:
f(x)=6(1.3)^-x
Then, we have
x = 10
This implies that
f(-10) = 6(1.3)^-(-10)
Evaluate the expression
f(-10) = 82.72
This means that the cost to heat is $82.72
Also, the domain is all set of real numbers and the range is y > 0
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Complete question
During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function
f(10)
work this out for points and brainliest !
a) The perimeter of a rectangle is the sum of all four sides. So to find the perimeter we can add these two sides together, and then double the result.
The simplified expression for the perimeter of the rectangle would be:
2(2n - 3 + 4)
This can also be written as:
2(2n + 1)
This expression represents the mathematical operation where the sum of 2n - 3 and 4 is calculated, then multiplied by 2 to find the perimeter of the rectangle.
b) If the perimeter of the rectangle is 26, we can use the expression for the perimeter that we found earlier to solve for the value of n.
The perimeter of the rectangle is:
2(2n + 1) = 26
So if we divide both sides of the equation by 2, we get:
2n + 1 = 13
then if we subtract 1 from both sides
2n = 12
then if we divide by 2
n = 6
So the value of n is 6.
I hope this helps :)
Answer:
a. [tex]P = 4n + 2[/tex]
b. [tex]n = 6[/tex]
Step-by-step explanation:
a. The formula for the perimeter of a rectangle was:
[tex]P = 2L + 2W[/tex]
Given that the length was 2n-3 and the width was 4, substitute the values its formula:
[tex]P = 2L + 2W\\P = 2(2n-3) + 2(4)\\P = 4n - 6 + 8\\P = 4n + 2[/tex]
b. Since the perimeter of the rectangle was already indicated, we will just sunstitute it to the expression that we get from a.
[tex]P = 4n + 2\\26 = 4n + 2\\26 - 2 = 4n\\24 = 4n\\6 = n[/tex]
The number of phone calls between two nearby cities during a given time period, N , varies directly as the populations P₁ and P₂ of the two cities. If 109,000 calls are made between two cities with populations 74,000 and 189,000, how many calls are made between two cities with population 125,000 and 175,000?
Answer:
170,483
Step-by-step explanation:
You have N varying jointly with P1 and P2, such that N=109,000 for P1=74000 and P2=189000. You want to know N for P1=125000 and P2=175000.
Varies jointlyThe relation "N varies jointly with P1 and P2" can be described by the equation ...
N = k·P1·P2
The value of k can be found as ...
k = N/(P1·P2)
k = 109000/(74000·189000) ≈ 7.793508×10^-6
New citiesThen the number of calls given the populations P1=125000 and P2=175000 is predicted to be ...
N = (7.793508×10^-6)(125000)(175000) ≈ 170482.982...
N ≈ 170483
About 170,483 calls are expected between cities with populations of 125 and 175 thousand.
If the number of phone calls between two nearby cities during a given time period. The number of calls that are made between two cities with population 125,000 and 175,000 is: 170,482,987,500.
How to find the number of calls?Calls made between two cities with populations 74,000 and 189,000,
Call = 109,000/(74000 × 189000)
Call = 109,000 / 13,986,000,000
Call = 7.793508
Calls made between two cities with populations 125,000 and 175,000?
Calls = 7.793508 × 125000 ×175000
Calls =170,482,987,500
Therefore the calls made is 170,482,987,500.
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which of the following fractions has been Simplified to lowest terms 25/95,21/49,3/17,10/15,44/52
3/17
Both 3 and 17 are prime numbers, therefore they cannot be simplified by any number expect 1 and itself.
Nevaeh has $2,131.50 in a savings account that earns 6% interest per year. If she initiall
deposited $2,100 how many months has she been investing her money?
We know that Nevaeh initially deposited $2,100, and now she has $2,131.50 in her account. The interest earned is $2,131.50 - $2,100 = $31.50. To find out how many months has she been investing her money, we can use the following formula:
Time (in months) = (Interest / Principal) x (12 / Interest Rate)
Where Principal is the initial deposit amount, Interest Rate is the annual interest rate, and Interest is the amount of interest earned.
Plugging in the given values, we get:
Time (in months) = ($31.50 / $2,100) x (12 / 0.06)
Time (in months) = 0.0149 x 200
Time (in months) = 2.98
Since time cannot be in fraction of months, it has to be rounded off. So, Nevaeh has been investing her money for approximately 3 months.
Round to nearest tenth show all work
Side AC in the triangle is 3.6 and side BC in the triangle is 1.7
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
To find side AC :
4/sin90 = AC / sin64.3
AC × sin90 = sin 64.3 × 4
AC = 0.9 ×4
AC = 3.6 ( nearest tenth)
To find side BC:
using Pythagoras theorem
4² = 3.6² + (BC)²
16 = 12.96 +(BC)²
(BC)² = 16 - 12.96
(BC)² = 3.04
BC = √ 3.04
BC = 1.7( nearest tenth)
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In planning her retirement, Liza deposits some money at
3.5%
interest, with twice as much deposited at
4.5%.
Find the amount deposited at each rate if the total annual interest income is
$1875.
Answer:
$15000 at 3.5%$30000 at 4.5%Step-by-step explanation:
You want to know the amounts invested at each rate if twice as much is invested at 4.5% as at 3.5%, and the total earnings are $1875.
Interest earnedLet x represent the amount invested at 3.5%. Then 2x is the amount invested at 4.5%, and the total earnings are ...
0.035x +0.045(2x) = 1875
0.125x = 1875 . . . . . . . . . collect terms
x = 15000 . . . . . . . . . divide by 0.125
2x = 30000 . . . . . . . find the other value invested
The amount deposited at 3.5% is $15,000; the amount deposited at 4.5% is $30,000.
Graph the piecewise function
The graph of the given piecewise function is as attached below.
Piecewise function is a function consisted of pieces of different functions over different intervals.
From the case we have:
f(x) = 3x - 5 if x ≤ -1
f(x) = -2x + 3 if -1 < x < 4
f(x) = 2 if x ≥4
To construct the piecewise function, we can try to find the base points of each functions.
f(x) = 3x - 5; if x ≤ -1
We will take x = -1 to approximate the line position
f(-1) = 3(-1) - 5
f(-1) = -3 - 5 = -8
f(x) = -2x + 3; if -1 < x < 4
(x = -1)
f(-1) = -2 (-1) + 3
f(-1) = 2 + 3 = 5
(x = 4)
f(4) = -2 (4) + 3
f(4) = -8 + 3 = -5
f(x) = 2; if x ≥ 4
(x = 4)
f(4) = 2
We can put each points on the graph and try to construct the piecewise function.
Please refer to the attached graph below for the piecewise function graph
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Jackie wants to buy a new van for work.
She wants to borrow £7,500 to buy the van and looks at two bank loans for this amount.
an image
Formula for simple interest is: I=PRT100
I
=
P
R
T
100
Formula for compound interest is: A=P(1+r100
A
=
P
(
1
+
r
100
)n
n
What is the difference in the interest charged between the two banks?
Answer: The interest rates charged in both formulas are different.
Step-by-step explanation:
To begin with, the simple interest = PRT/100
In this, the interest is the same as the number of years.
For example, P=10,000 R=10% T=2yrs
SI = PRT/100
= 10,000*10*2/100
= 2000
This rupee 2000 is the same interest for two years.
compound interest = A= P(1+r/100)^n
In this, the interest changes every year up to the period of time.
For example, P= 10,000 R=10% N=2yrs
A= 10,000(1+10/100)^2
= 10,000*11/10*11/10
= 12100
I= A-P
=12100-10000
= 2100
This interest varies for 2 years.
Which angle corresponds to <8?
Answer:
>4
Step-by-step explanation:
the answer of the question is >4
112 divide by 0.16 with solutions
The solution for the expression 112 ÷ 0.16 is 700.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
112 ÷ 0.16
This can be written as,
= 112/0.16
= 700
Thus,
The solution is 700
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Calculate midpoint 6 for f(x)= 6 * ln(x^2) over [1,2]
The midpoint of f(x) over the interval [1, 2] is 4.8655
What is the midpoint of an interval?Generally, The point that represents the precise midway point between an interval's beginning and ending points is known as the midpoint of the interval. It may be determined by calculating the average of the two values that serve as endpoints.
For instance, the value 5 would represent the point that is exactly in the middle of the interval [3,7].
The midpoint of the interval [1, 2] is
(1 + 2) / 2
= 1.5.
To calculate the value of f(x) at x = 1.5, we need to substitute 1.5 for x in the function:
f(1.5) = 6 * ln(1.5^2)
= 6 * ln(2.25)
= 6 * 0.83
= 4.8655
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In the following descriptions of a study, confounding in present. Describe the explanatory and confounding variable in the study and how the confounding may invalidate the conclusions of the study. Furthermore, suggest how you would change the study to eliminate the effect of the confounding variable.
(a)A hospital introduces a new blood clot medication that can be given to the patients suffering from a stroke during the crucial period of 12 hours after stroke begins. The new medication appears to be very successful because in the first year of its implementation there is a higher rate of total recovery by the patients in comparison to the rate in the previous year for patients admitted to the hospital.
(b) A high school mathematics teacher is convinced that a new software program will improve math scores for students take the SAT. As a method of evaluating her theory, she offers the students opportunity to use the soft-ware on the school’s computers during a 1-hour period after school. The teacher concludes the software is effective because the students using the software has significantly higher scores on the SAT than did the students who did not use the software.
a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.
b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school
What are the variables?The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.
In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.
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PLS PLS HELp, i dont get what it means by for
Answer:
don't
Step-by-step explanation:
get that one wrong don't spend to much time on it
On Friday, Wall Street traders were anxiously awaiting the federal government's release
of numbers on the January increase in nonfarm payrolls. The early consensus estimate
among economists was for a growth of 250,000 new jobs (CNBC, February 3, 2006).
However, a sample of 20 economists taken Thursday afternoon provided a sample mean
of 266,000 with a sample standard deviation of 24,000. Financial analysts often call such
a sample mean, based on late-breaking news, the whisper number. Treat the "consensus
estimate" as the population mean. Conduct a hypothesis test to determine whether the
whisper number justifies a conclusion of a statistically significant increase in the consen-
sus estimate of economists. Use a = .01 as the level of significance.
Anazlysing the conditions given in the question we can conclude that there is a statistically significant increase in the consensus estimate of economists.
How do financial analysts use the whisper number in their decision making process?Financial analysts often use the whisper number, which is a late-breaking estimate of a key economic indicator, to make predictions about the stock market and inform their investment decisions. They may use it to identify potential opportunities for buying or selling stocks based on whether the whisper number is higher or lower than expected.
Can the whisper number be used to predict the stock market?While the whisper number can provide insight into the current economic conditions, it is not a foolproof way to predict the stock market. It is just an estimate based on a sample of economists' predictions and can be affected by various unpredictable factors. Therefore, it's important to take other economic indicators and market conditions into account when making investment decisions.
To conduct a hypothesis test, we need to first define the null hypothesis and alternative hypothesis.
Null Hypothesis: The whisper number (sample mean) is equal to the consensus estimate (population mean)
H0: μ = 250,000
Alternative Hypothesis: The whisper number (sample mean) is greater than the consensus estimate (population mean)
H1: μ > 250,000
The next step is to calculate the test statistic and p-value. We can use a one-tailed t-test since the sample size is less than 30 and we don't know the population standard deviation.
Test statistic:
t = (266,000 - 250,000) / (24,000 / sqrt(20))
P-value:
Using the t-distribution table with 19 degrees of freedom, the p-value is less than 0.01, which is the significance level we set.
Since the p-value is less than the significance level (0.01), we can reject the null hypothesis and conclude that there is a statistically significant increase in the consensus estimate of economists.
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. A bicycle store uses a young person's height as one factor to determine the wheel diameter of an appropriate bicycle. For heights of 44-48 inches , the store suggests 18 inch wheels. For heights of 47-53 inches, the store suggests 20 inch wheels. For heights of 52-57 inches , the store suggests 24 inch wheels. Is the relationship between a young person's height and the recommended wheel diameter a function? Explain your reasoning.
The relationship between a young person's height and the recommended wheel diameter is a function, as each input is associated to a single output.
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
The input and output variables for this problem are given as follows:
Input variable: young person's height.Output variable: recommended wheel diameter.As for each height, there is only one recommended wheel diameter, we have that each input is mapped to a single output, and thus the relationship between a young person's height and the recommended wheel diameter is a function.
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HELP PLSS
Find the difference: √20-√80
O -12,5
O-2√5
O2√5
O-2√15
DONE✔
Answer:
[tex] - 2 \sqrt{5} [/tex]
Step-by-step explanation:
[tex] \sqrt{20} - \sqrt{80} [/tex]
[tex]2 \sqrt{5} - 4 \sqrt{5} [/tex]
[tex](2 - 4) \sqrt{5} [/tex]
[tex] - 2 \sqrt{5} [/tex]
I have 18 students that took a test. 4 of the students passed. What is the percentage of the students that passed and the students that didn't pass?
Step-by-step explanation:
as always with % calculations :
first find what is 100% or 1%. everything else can be calculated from that.
in our case, we got 100% = 18.
therefore, 1% = 100%/100 = 18/100 = 0.18
how many % are 4 students ?
as many as the times 1% (0.18) fits into 4 :
4 / 0.18 = 22.22222222... %
so,
22.22222222... %
of the students passed.
therefore,
100 - 22.22222222... = 77.77777777... %
of the students did not pass.
A manufacturing firm want to determine the proportion of defects in a manufacturing process. How many of its products does it need to sample if it wants to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%?
The firm needs to sample 138.297 products to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%.
What is a manufacturing firm?Generally, To determine the sample size needed to achieve a ±5% accuracy at a 95% confidence level, with a maximum expected proportion of defects of 10%, you can use the formula for sample size for a proportion. The formula is:
n = (z^2 * p * (1-p)) / E^2
Where:
n is the sample sizez is the standard normal deviate corresponding to the desired level of confidence (1.96 for a 95% confidence level)p is the maximum expected proportion of defects (0.10 in this case)E is the margin of error (0.05 in this case)Plugging in the given values, we get:
n = (1.96^2 * 0.10 * (1-0.10)) / 0.05^2
n =138.297
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Problem in the attached image! Pls help only 10 and 11
The alternate interior angles are the angles that are formed inside the two parallel lines, when it is intersected by a transversal, and are equal to its alternate pairs.
What is alternate interior angles?Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.
Alternate angles are shaped by the two parallel lines crossed by a transversal. Consider the given figure, EF and GH are the two parallel lines. If two parallel lines are cut by a transversal, then the alternate angles are equal.
In order to understand alternate interior angles, one must first picture a set of parallel lines, and then a line intersecting them. The intersecting line is called a transversal, and all the angles formed between the parallel lines are the interior angles.
At the point of intersection of transversal and two lines we have:
∠3 + ∠4 = 180 .........(1)
∠6 + ∠8 = 180 ...........(2)
We know that angle 4 and angle 8 are equal:
Thus, using 1 and 2 we have:
∠3 = ∠6
Hence, ∠3 and ∠6 are congruent.
Now, using the alternate interior angle we know that:
∠3 = ∠6
Also, we have:
∠5 + ∠6 = 180 (Straight line)
Substituting the value of ∠6 = ∠3 we have:
∠5 + ∠3 = 180
Thus, the two angles are supplementary.
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Huilan is 14 years older than Thomas. The sum of their ages is 113. What is Thomas age
Answer: 49.5
Step-by-step explanation:
Let Thomas' age be [tex]T[/tex]. Then, Hulian's age is [tex]T+14[/tex].
[tex]T+T+14=113\\\\2T+14=113\\\\2T=99\\\\T=49.5[/tex]
Are these triangles similar?
O Yes
O No
By which way are the triangles
similar?
O AA Similarity
O The triangles are not similar.
O SSS Similarity
O SAS Similarity
Answer:no
Step-by-step explanation:
Please please look at the picture and answer the question thank you
Answer:
[tex]\boxed{-2 < x\le1}[/tex]
Representation on number line is in attached image.
Notice that -2 has an unfilled circle and 1 has a filled circle. Important
Step-by-step explanation:
The given inequality is
[tex]2 < 4x+10\le14[/tex]
Subtract 10 throughout:
[tex]2-10 < 4x+10-10\le14-10\\\[/tex]
[tex]-8 < 4x\le4[/tex]
Divide throughout by 4:
[tex]-2 < x\le1[/tex]
Answer: [tex]\boxed{-2 < x\le1}[/tex]
This is represented on the number line as follows: Notice the use of the
there are 28 questions on a test i got 16 wrong what percent did i get correct? round to the nearest percent
Answer:
43%
Step-by-step explanation:
28 questions - 16 wrongs = 12 correct
(12/28) × 100= 42.857.....%
To the nearest percent=43%
The prism shown has a volume of 35 cm³.
Work out h, the height of the triangular cross section.
Optional working
h
base = 4 cm
Length = 7 cm
[tex]35 cm ^{3}[/tex] is the volume of the prism displayed. The triangular cross section is 1.25 cm tall.
What is the height of the prism ?length , l = 7 cm , width w = 4 cm , height , h= 1.25 ,diagonal , d=8.15858444 cm , total surface area, [tex]$S_{\text {tot }}=83.5 \mathrm{~m}^2$[/tex] , lateral surface area , [tex]$S_{\text {lat }}=27.5 \mathrm{~m}^2$[/tex] , top surface area , [tex]$S_{\text {top }}=28 \mathrm{~m}^2$[/tex] , bottom surface area , [tex]$S_{\text {bot }}=28 m^2$[/tex] , volume [tex]$V=35 \mathrm{~m}^3$[/tex] .
To calculate the height of a prism, divide its volume by its area at the base. Let's say that the prism has a volume of 600 cubic inches to wrap up this scenario. The height is determined by multiplying 600 cubic inches by 100 square inches.
A prism's volume is calculated using the formula V=Bh, where B denotes the base area and h the height. A rectangular area makes up the prism's base. The rectangle's dimensions are 9 cm long by 7 cm wide. The formula V=Bh, where V stands for volume, B for the prism's area at its base, and h for its height, can be used to determine a prism's volume. B should be replaced with the area of a rectangle formula because this is a rectangular prism.
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Given these observed times (in minutes) for five elements of a job, determine the observed time (OT) for each element. Note: Some of the elements occur only periodically.
The observed time cycles of five given elements are 2.1, 1.01, 3.4, 4.1, 1.5 respectively
How to determine the observed time?To determine the observed time (OT),
The observed time (OT) of each cycles will be added together for each element. and divided by total number of cycles for each element.
This is done in the following ways
1) (1.2+2.0+2.2+2.1+2.1)/5 = 10.5/5 = 2.1
2) (1.1+1.0+1.2) = 3.3/3 = 1.1
3) (3.4+3.5+3.3+3.5+3.4+3.3)/6 = 20.1/6 = 3.4
4) 4.0+4.2)/2 = 8.2/2 = 4.1
5) (1.4+1.4+1.5+1.5+1.5+1.4)/6 = 8.7/6 = 1.5
therefore each elements total cycle OT is added and then it is divided with each elements relevant number of cycles and this as a result provides the answer to the question
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Solve for the interior of angle, x.
90°
130°
130⁰
130
120%
Xo
Provide the reasons for the following proof.
The figure shows triangle W X Y with a segment X Z drawn from vertex X to point Z on side W Y.
Given: Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y
Prove: triangle W X Z is congruent to triangle Y X Z
Statements Reasons
1.Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y 1. Given.
2. angle W X Z is congruent to angle Y X Z 2. Definition of an angle bisector.
3. Segment X Z is congruent to segment X Z. 3. _____________
4. triangle W X Z is congruent to triangle Y X Z 4. _____________
A. Reflexive Property of congruent to; SSS
B. Symmetric Property of congruent to; SSS
C. Reflexive Property of congruent to; SAS
D. Symmetric Property of congruent to; SAS
SOMEONE HELP! PLEASE!
The two column proof showing that ΔWXZ ≅ ΔYXZ is as shown below
From the given triangle, we see that;
Given: WX ≅ XY, XZ bisects WXY
Prove: ΔWXZ ≅ ΔYXZ
The two column proof for the above is as follows;
Statement 1; WX ≅ XY, XZ bisects 2
Reason 1; Given
Statement 2: ∠WXZ ≅ YXZ
Reason 2; Angle bisector
Statement 3; XZ ≅ XZ
Reason 3: Reflexive property of congruence
Statement 4: ΔWXZ ≅ ΔYXZ
Reason 4: SAS Congruence Postulate
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A pyramid has a(n) for a base and a number of that all meet at the
same
о
-
A. two-dimensional object; faces; vertex
B. point; vertices; point
C. polygon; edges; face
D. edge; faces, point
Answer:
B. point; vertices; point
Step-by-step explanation:
A pyramid is a 3-dimensional geometric shape that has a base, which is typically a polygon, and a number of triangular faces that all meet at a single point called the vertex. The pyramid has vertices at the corners of the base and all other points where the triangular faces meet.
