the area of the base (B) of a triangular pyramid is 28 cm. The perimeter (p) is 20 cm, and the slant height (S) is 5 cm. Determine the pyramid's surface area. A) 96 cm2 B) 128 cm2 C) 225 cm2 D) 78 cm2

Answer:

81

Step-by-step explanation:

ANGLES in a TRIANGLE add up to 180

In the Triangle you have 65 and 34

Add them together = 99

Subtract the total from 180

180 - 99 = 81

Answer:

81 degrees

Step-by-step explanation:

The angles of the triangle always add up to 180.

SO you'd do 65+34 which equals 99.

NOW you do 180-99 which equals 81

So you're missing angle would be 81 degrees

Answer:

Part A - 4x + 8 dollars

Part B - $45

Step-by-step explanation:

Answer:

4,212

Step-by-step explanation:

Step 1:  Add

23 + 4189

4,212

Answer:  4,212

Answer:

12x⁴ + 2x³ + x² - 7x + 14

Step-by-step explanation:

(5x^4-3x^3+2x^2-15x+27) + (7x^4+5x^3-x^2+8x-13)

(5+7)x⁴ + (-3+5)x³ + (2-1)x² + (-15+8)x + (27-13)

12x⁴ + 2x³ + x² - 7x + 14

Answer:

The change in total amount of money the cashier are paid each week will be $331.5.

Step-by-step explanation:

16 store cashiers work average 21 hours per week and paid $8.25 per hour.

Now, the store manager hires 2 additional cashiers each cashier will be paid 0.25 more per hour and will work an average of 1.5 fewer hours per week.

Therefore, the two additional cashiers will be paid $8.50 per hour and will work an average of (21 - 1.5) = 19.5 hours per week.

So, the change in the total amount of money the cashiers are paid each week will be (2 × 19.5 × 8.5) = $331.5. (Answer)

Answer: 373/50

Step-by-step explanation:

Step 1: convert to a fraction

746% = 746 ÷ 100 = 7.46

7.46 = 373/50

Step 2: Write the number as a fraction of one: 7.46 = 746/100

Step 3: use a common divisor of 2 to reduce the numbers, we have

(746÷2)= 373

(100÷2)=50

when reduced to the simplest form= 373/50

Therefore, 746/ 100 = 373/50 when expressed as a mixed number.

Answer: 373/50

Step-by-step explanation:

Step 1) Since 746% is a percent, it is written over the denominator of 100. So first convert it to a fraction, which would be 746/100.

Step 2) Find the GCF (greatest common factor). In order to find the GCF start by writing all the factors of

100:

1, 2, 4, 5, 10, 20, 25, 50, 100

Step 3) Now test every number there and see if any go into 746. Start at the highest number, which in this case is 100. (Example, ask yourself, “does 100 go into 746? No.” Then try with 50, and continue until you get to a number that goes into 746 evenly.)

Step 4) The GCF from the previous step is 2. So now divide 746 by 2 (answer is 373) and 100 by 2 (answer is 50).

Step 5) Now put 373/50 and that’s your answer! Congratulations you finished it!

Answer:

When I calculated this I got: 4.2857142857143 but I don't know if that's the correct answer.

Step-by-step explanation:

Answer:

l=48, w=20

Step-by-step explanation:

Let the width of the pool be w feet, then the length will be:

[tex]l = 2w + 8[/tex]

The area of the pool is 960 square feet.

This means that:

[tex]w(2w + 8) = 960[/tex]

Expand and rewrite in standard form to get:

[tex]2 {w}^{2} + 8w - 960 = 0[/tex]

[tex] {w}^{2} + 4w - 480 = 0[/tex]

[tex]{w}^{2} + 24w - 20w- 480 = 0[/tex]

[tex]{w}(w+ 24) - 20(w + 24) = 0[/tex]

Factor to get:

[tex](w+ 24)(w - 20) = 0[/tex]

[tex]w = - 24 \: or \: w = 20[/tex]

We discard the negative value because magnitude is positive.

This means

[tex]l = 2 \times 20 + 8 = 48[/tex]

Probability of distinct 3-digits is 1/6.

Probability of both the first digit and the last digit are even numbers is 1/5.

Step-by-step explanation:

Given set of numbers {1,2,3,5,8,9} = 6

Total number of 3-digits can be formed = 6[tex]\times[/tex]5[tex]\times[/tex]4 = 120.

Probability  of the three-digit numbers with distinct digits :

The number of 3-digit numbers with distinct digits = (6[tex]\times[/tex]5[tex]\times[/tex]4) / (3[tex]\times[/tex]2[tex]\times[/tex]1) = 20.

P(distinct 3-digits) =  no. of distinct 3-digits / Total no.of 3-digits

⇒ 20/120

⇒ 1/6

Probability that both the first digit and the last digit of the three-digit number are even numbers :

The even numbers in the set are 2 and 8 = 2 possibilities.

The number of 3-digits with 1st and 3rd digit are even = (2[tex]\times[/tex]6[tex]\times[/tex]2) = 24.

P(1st and 3rd digits even)= no. of 1st and 3rd digit even/Total no. of 3-digits.

⇒ 24/120

⇒ 1/5

Answer:

3)1 unit right and 1 unit down

Step-by-step explanation:

The parent function is

[tex]y = |x| [/tex]

This is the base of the absolute value functions.

It has its vertex at the origin.

The transformed function is

[tex]y = |x - 1| - 1[/tex]

This absolute value function has its vertex at (1,-1).

This means the parent function has been shifted 1 unit right and 1 unit down to obtain the transformed function.

Answer:

Step-by-step explanation:

volume =1/3×base area×height

216=1/3× A×6

base area=216/2=108 in²

Answer:

Here is the answer

Step-by-step explanation:

108 in squared

or D

Answer:

the height is 3

the with is also 3 because

1.5+1.5=3

Answer:

This question would be related to slopes so the answer is [tex]y=-\frac{7}{2}x+\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\mathrm{Slope-Intercept\:form\:of}\:\\x2+y2+12x+2y-1=0:\quad y=-\frac{7}{2}x+\frac{1}{4}[/tex]

[tex]\mathrm{Domain\:of\:}\:-\frac{7}{2}x+\frac{1}{4}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Range\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Parity\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{Neither\:even\:nor\:odd}[/tex]

[tex]\mathrm{Axis\:interception\:points\:of}\:\\-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{14},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\frac{1}{4}\right)[/tex]

[tex]\mathrm{Inverse\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad -\frac{4x-1}{14}[/tex]

[tex]\mathrm{Slope\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad m=-\frac{7}{2}[/tex]

Hope this helps you!

Have a good night!

The chances of winning the grand prize in this game are approximately 0.089, whereas the chances of winning the consolation prize are 0.01.

The subject of this question is Probability, which is a branch of Mathematics. To calculate the probability, we'll need to determine the total number of outcomes and the count of the favorable outcomes.

a) To win the grand prize, all three balloons popped have to have 'Winner' slips. The probability of each dart hitting such a balloon will decrease as the total number of balloons decreases. First dart probability would be 5/8 (5 'Winner' balloons out of 8 total), the second one 4/7 (as one 'Winner' balloon is already popped), and 3/6 for the third. Multiply these probabilities together to get the overall probability: (5/8) * (4/7) * (3/6) = 0.089 (rounded to the third digit).

b) Similarly, for the consolation prize, we would have to hit all three balloons with blank slips. The process is equivalent, resulting in a probability of (3/8) * (2/7) * (1/6) = 0.01 (rounded to the third digit).

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Answer:

494 square feet

494 ft^2

Step-by-step explanation:

Trapezoid:

(20 + 32) ÷ 2 ) × 3

52 ÷ 2 ) × 3

26 × 3

= 78

Rectangle:

32 × 13 = 416

Add:

78 + 416 = 494

The slope represents the rate of change. Then the rate of change will be 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = 4x + 60

The slope is 4 and the y-intercept is 60.

The slope represents the rate of change. Then the rate of change will be 4.

More about the linear equation link is given below.

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The rate of change in the equation y = 4x + 60 is 4, which is the coefficient of x. This means for each unit increase in 'x', 'y' will increase by 4 units.

In mathematics, the rate of change in an equation like y = 4x + 60 is represented by the coefficient of the variable x. This is because, in such an equation which is in the form of y = mx + b (a standard linear equation), 'm' represents the rate of change or the slope of the line.

So, in your specific equation y = 4x + 60, the rate of change or slope is 4. This means that for each increment of 1 in 'x', 'y' will increase by 4 units. This value - 4 - is your rate of change in this case.

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Circumference of the circle = 94.2 yd

Solution:

Given data:

Diameter of the circle = 30 yd

The value of π = 3.14

To find the circumference of the circle:

Circumference of the circle = πd

Substitute the diameter value in the formula, we get

Circumference of the circle = 3.14 × 30

                                              = 94.2

Circumference of the circle = 94.2 yd

(12, 11):

2((12) + 3) - (11) = 7 + (12)

2 • 15 - 11 = 19

2 • 4 = 19

8  [tex]\neq[/tex]  19

(1, 0):

2((1) + 3) - (0) = 7 + (1)

2 • 4 = 8

8 = 8

(-5, 1):

2((-5) + 3) - (1) = 7 + (-5)

2 • -2 - 1 = 2

2 • -3 = 2

-6  [tex]\neq[/tex]  2

Hope this helps.

Answer:

Step-by-step explanation:

a) (5,5) ;    (10,6);  slope = 1/5

  (x1,y2);    (x2,y2)

y-y1 = m (x-x1)

[tex]y-5=\frac{1}{5}*(x-5)\\\\y-5=\frac{1}{5}*x-\frac{1}{5}*5\\\\y-5=\frac{1}{5}x-1\\y=\frac{1}{5}x-1+5\\\\y=\frac{1}{5}x+4[/tex]

d) (√2,7)    ; (√2,-7)

  (x1,y1)    ; (x2,y2)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-7-7}{\sqrt{2}-\sqrt{2}}\\\\=\frac{-14}{0}=0[/tex]

Equation: y =7 or y = -7

Answer:

If it is a six-sided die then it has the probability of 1/6 or .16

Step-by-step explanation:

Answer:

1) 5.313131 put the bar over the first 31

2)0.999 put the bar over the first 9

3)2.010101 put the bar over the first 01

4)26.993993 put the bar over the first 993

Step-by-step explanation:

Answer:

The answer should be 45

Step-by-step explanation:

To get the whole are you would have to multiply the lenght with the Width and then take that answer and multiply it with the height

BUT

because you want the surface area, it would be just the lenght and width

15x3=45

so 45 is your answer.

The formula [tex]3(4^{n-1})[/tex] represents the geometric sequence.

Step-by-step explanation:

Step 1:

The value of [tex]a_{n}[/tex] is dependent on the value of n.

So n is independent while [tex]a_{n}[/tex] is dependent on n i.e. the value of [tex]a_{n}[/tex]depends on the value of n.

Step 2:

We substitute the values of n in the functions to check which function satisfies the values of [tex]a_{n}[/tex].

If [tex]n = 4, a_{n} = -4(3)^{n-1} = -4 (3^{3}) = -108.[/tex] This does not equal the value of [tex]a_{n}[/tex].

If [tex]n = 4, a_{n} = 4(3)^{n-1} =-4 (3^{3}) = 108.[/tex] This does not equal the value of [tex]a_{n}[/tex].

If [tex]n = 4, a_{n} =3(-4)^{n-1} = 3 (-4^{3}) = -192.[/tex] This does not equal the value of [tex]a_{n}[/tex].

If [tex]n = 4, a_{n} =3(4)^{n-1} = 3 (4^{3}) = 192.[/tex] This equals the value of [tex]a_{n}[/tex].

So the fourth formula represents the geometric sequence.

When doing absolute value, negatives will always be positive.

Option A's absolute value is 140.

Option B's absolute value is 104.

Option C's absolute value is also 104.

Option D's absolute value is 204.

Therefore, the option with the greatest absolute value would be D. |-204|

Answer:

A because is positive and highlights numbers

Answer:

1 pencil = $0.75

1 eraser = $0.29

Step-by-step explanation:

4p+2e=3.58                                 1p+6(0.29)=2.49

1p+6e=2.49                                   1p+1.74=2.49

p=2.49-6e                                     1p=0.75

4(2.49-6e)+2e=3.58                       p=0.75

9.96-24e+2e=3.58

9.96-22e=3.58

-22e=-6.38

e=0.29

Initial equation:

4a / 2 = 5.2

Multiply both sides by 2:

4a = 10.4

Divide both sides by 4:

a = 2.6

Hope this helps!! :)

Answer:

Step-by-step explanation:

2.6 becuase 4a/2= 5.2

4a=10.4

a=2.6

Answer:

531.

Step-by-step explanation:

Let's assume 2(1) + 1 = 3

a = 1 and b = 1

Now we can plug that in

8(1)^3 + (1)^3 + 18(1)(1)

Then we need to multiply together

8^3 + 1^3 + 18

Then do the powers

512 + 1 + 18

Then add them together

531

Hope this helped!

Answer:

27

Step-by-step explanation:

A sum of cubes factors as

a³ + b³ = (a + b)(a² - ab + b²)

Factor the sum of cubes 8a³ + b³

8a³ = (2a)³, thus

8a³ + b³

= (2a)³ + b³

= (2a + b)(4a² - 2ab + b²)

We now have the right side as

(2a + b)(4a² - 2ab + b²) + 18ab ← substitute 2a + b = 3

= 3(4a² - 2ab + b²) + 18ab

= 12a² - 6ab + 3b² + 18ab ← collect like terms

= 12a² + 12ab + 3b² ← factor out 3 from each term

= 3(4a² + 4ab + b²) ← perfect square

= 3(2a + b)² ← substitute 2a + b = 3

= 3 × 3²

= 3 × 9

= 27

Answer:

Step-by-step explanation:

Let w be the width

Length = 3w +15

Perimeter = 94 cm

2*(length + width) = 94

2*(3w+15 + w) = 94

2*( 4w + 15) = 94

4w + 15 = 94/2

4w +15 = 47

        4w = 47 -15

         4w = 32

           w = 32/4

          w = 8 cm

Length = 3w +15 = 3*8 + 15 = 24 +15 = 39

Length = 39cm

Area = length * width = 39*8 = 312

Area = 312 cm²

The area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]

Step 1

Let's denote the width of the rectangle as w cm.

According to the problem, the length of the rectangle is [tex]\( 15 \)[/tex] cm more than three times its width. So, the length [tex]\( l \)[/tex] can be expressed as [tex]\( 3w + 15 \)[/tex]cm.

The perimeter P of a rectangle is given by:

[tex]\[ P = 2(l + w) \][/tex]

Given that the perimeter of the rectangle is [tex]\( 94 \)[/tex] cm, we can write the equation:

[tex]\[ 94 = 2((3w + 15) + w) \][/tex]

Step 2

Now, let's solve for [tex]\( w \)[/tex]:

[tex]\[ 94 = 2(4w + 15) \]\[ 94 = 8w + 30 \]\[ 8w = 94 - 30 \]\[ 8w = 64 \]\[ w = \frac{64}{8} \]\[ w = 8 \][/tex]

Step 3

Now that we have found the width of the rectangle to be [tex]\( 8 \)[/tex] cm, we can find its length:

[tex]\[ l = 3w + 15 \]\[ l = 3(8) + 15 \]\[ l = 24 + 15 \]\[ l = 39 \][/tex]

Step 4

Now that we have the width [tex]\( w = 8 \)[/tex] cm and the length [tex]\( l = 39 \)[/tex] cm, we can calculate the area A of the rectangle:

[tex]\[ A = l \times w \]\[ A = 39 \times 8 \]\[ A = 312 \][/tex]

So, the area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]

The account balance will be $6642 after seven years.

Step-by-step explanation:

To find the amount after seven years, a certain formula is used.

Amount = [tex]P( 1+r/n)^{n\times t}[/tex]

where,

P is the principal amount that is invested in the account.

Therefore, P = 4500 dollars.

r is the rate of interest. (r = 5.5 %)

Therefore, r = 5.5/100 = 0.055

n is the number of time the interest is compounded per year which is n= 4.

t is the time period which is t = 7 years.

Now, substituting all the above values in the formula,

Amount = [tex]4500(1+0.055/4)^{4\times 7}[/tex]

⇒ [tex]4500(4.055/4)^{28}[/tex]

⇒ [tex]4500(1.014)^{28}[/tex]

⇒ [tex]4500\times1.4759[/tex]

⇒ 6641.55 (which is approximately equal to 6642)

⇒ 6642 dollars.

The account balance after 7 years is $6642.

Answer:$125

Step-by-step explanation:

50% of 250

50/100 x 250

1/2 x 250=(1x250)/2=250/2=125