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3 years ago

A convex polyhedron has (a + 3) faces, (2a) vertices, and (4a – 1) edges. What is the value of a? a =

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

7 0

Answer:

a = 2

Step-by-step explanation:

BECAUSE I'M CORRECT!

rusak2 [61]3 years ago

4 0

Number of faces: F=a+3
Number of vertices: V=2a
Number of edges: E=4a-1

V+F-E=2
Replacing V=2a; F=a+3; and E=4a-1 in the formula above:
(2a)+(a+3)-(4a-1)=2
Eliminating parentheses:
2a+a+3-4a+1=2
Adding similar terms:
(2+1-4)a+(3+1)=2
(-1)a+4=2
Solving for a. Subtracting 4 both sides of the equation:
(-1)a+4-4=2-4
(-1)a=-2
Dividing both sides by (-1)
(-1)a/(-1)=-2/(-1)
a=2

Answer: The value of a is: a=2

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can some one explain to me how fractions work who ever explains it well gets brainliest, adding, subtracting, multiplying, divid

Ludmilka [50]

Adding: When adding fractions, you want to make sure that the denominator is the same for both fractions. If they are already the same, just add both the numerators to get the answer. For example,
$\frac{3 }{5} + \frac{1}{5} = \frac{4}{5}$
If the denominator is different in both fractions, you have to find the least common denominator, or LCD. The LCD is the smallest number that both denominators can multiply into. For example, say you need to find
$\frac{1}{6} + \frac{1}{3}$

Multiply both the numerator and the denominator of (1/3) by 2 to get (2/6). This way, the denominators are the same and you can find the answer.
$\frac{1}{6} + \frac{2}{6} = \frac{3}{6}$
In the case that one denominator does not go into the other, find the smallest number they both multiply into. For example,
$\frac{1}{3 } + \frac{1}{4}$
Here, the smallest number that both 4 and 3 multiply into is 12. Multiply both fractions by the correct amount to make both denominators 12. It would then become
$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
Subtraction: follow the same rules as addition, except subtract the numerators instead of adding them.

Multiplication: multiply both numerators and both denominators.
$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$
Division: Flip one of the fractions and multiply.
$\frac{2}{3} \div \frac{4}{5}$
Becomes
$\frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$
Hope this explains it all. Let me know if you have any questions :)

4 0

3 years ago

Vanessa deposits $24,000 into each of two savings accounts. Account I earns 2. 4% interest compounded annually. Account II earns

ikadub [295]

The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

<h3>How to calculate compound interest's amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

$CI = P(1 +\dfrac{R}{100})^T - P$

The final amount becomes:

$A = CI + P\\A = P(1 +\dfrac{R}{100})^T$

<h3>How to calculate simple interest amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

$I = \dfrac{P \times R \times T}{100}$

For the considered case, we're given that:

Initial amount in both accounts deposited = $24,000 = P
Type of interest: Compound interest in first account and simple interest in second account
Unit of time: Annually
Rate of interest = 2.4% annually = R
Total unit of time for which amount is to be calculated: 5 years = T

In first account, the final amount at the end of 5 years is evaluated as:

$A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4 \approx 27021.59\: \rm (in \: dollars)$

In second account, the final amount at the end of 5 years is evaluated as:

$A = 24000 + \dfrac{24000 \times 2.4 \times 5}{100} = 24000 + 2880 = 26880 \text{\: (in dollars)}$

Total amount after 5 years in these accounts = $27021.59 + 26880 = 53901.59$ (in dollars)

Thus, the sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

Learn more about compound interest here:

brainly.com/question/11897800

4 0

2 years ago

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 60 o

krok68 [10]

Answer:

a) 99.7% of the widget weights lie between 45 and 75 ounces

b) 97.2% of the widget weights lie between 50 and 75 ounces

c) 84% of the widget weights lie above 55

Step-by-step explanation:

The Empirical Rule states that:

50% of the values of a measure is above the mean, and the other 50% is below the mean.

99.7% of the values of a measure lie between 3 standard deviations of the mean.

95% of the values of a measure lie between 2 standard deviations of the mean.

68% of the values of a measure lie between 1 standard deviations of the mean.

In this problem, we have that: The widget weights have a mean of 60 ounces and a standard deviation of 5 ounces.

(a) 99.7% of the widget weights lie between

3 standard deviations of the mean, so:

60 - 3*5 = 60 + 3*5 = 45 and 75 ounces

(b) What percentage of the widget weights lie between 50 and 75 ounces?

We have to find the percentage that are below 75 and subtract by the percentage that are below 50. So

75 is 3 standard deviations above the mean. So 99.7% of the measures are below 75.

50 is 2 standard deviations below the mean. So only 5% of the measures that are below the mean are below 50.

99.7% - (50%)5% = 99.7% - 2.5% = 97.2%

(c) What percentage of the widget weights lie above 55?

55 is one standard deviation below the mean.

50% of the widget weights are above the mean.

Of the 50% that is below, 68% lie between one standard deviation(So from 55 to 60)

50% + 68%(50%) = 84%

3 0

3 years ago

Sarah is cutting ribbons for a pep rally the length of each ribbon needs to be 3.72 inches if she needs 1,000 ribbons what is th

HACTEHA [7]

If she needs 1,000 ribbons at 3.72 inches each, She will need 1,000 x 3.72 which equals 3720 inches of ribbon.

This can be converted into feet by taking 3720 inches and dividing by 12 inches in a foot.

This will an answer of 310 feet.

7 0

3 years ago

Help Please Worth 20 points

Romashka [77]

17 ft, 8:20 , 39ft , 9:08

your welcome!

3 0

3 years ago

Read 2 more answers