A fair six-sided die is tossed. After it lands, the bottom face cannot be seen. What is the probability that the product of the visible numbers on the five faces is divisible by 12?

Answer:

see explanation

Step-by-step explanation:

This is an arithmetic sequence with n th term

• [tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 2 - 7 = - 3 - 2 = - 5 and a = 7, hence

[tex]a_{n}[/tex] = 7 - 5(n - 1) = 7 - 5n + 5 = 12 - 5n

[tex]a_{n}[/tex] = 12 - 5n ← n th term formula

Answer: The answer is 7√3

Step-by-step explanation:

Since the hypotenuse is twice as long as the shortest leg and the triangle is 30°-60°-90°, therefore the shortest leg is 7 (not the answer to your question) and the other leg is 7√3. I hope this helps :)

Answer:

Step-by-step explanation:

I just did this question and this was the answer that was right for me :) Hope this helps!

Answer:

D

Step-by-step explanation:

D would be the correct answer because the x values have their individual y values. D is the only answer where the x point doesn't repeat, and the only time it can repeat is if the x points have the same y value such as: (2,4) (2,4)

For each value of x, the value of y is different. Then the correct option is D.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

Individual y values exist for each of the x values. The only instance the x point can recur is if the x locations have about the same y value, as in D. (2,4).

Then the points represents a function is (1, 7), (2, 1), (5, 3), (4, 9), (6, 3).

Thus, the correct option is D.

More about the function link is given below.

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Answer:

As a proper fraction  - 39/51 = 13/17

As a decimal number:  39/51 ≈ 0.76

As a percentage:  39/51 ≈ 76.47%

Step-by-step explanation:

Calculate the greatest (highest) common factor (divisor), gcf (gcd).

13/17 =

13 ÷ 17 =

0.764705882353 ≈

0.76

By precentage

0.764705882353 =

0.764705882353 × 100/100 =

76.470588235294/100 =

76.470588235294% ≈

76.47%

Answer:

Angle A measures 180° - (24° + 55°) = 180° - 79° = 101°.

Angle x measures 360° - 101° = 259°.

The answer will be $29.02. :)

Answer:

$29.02.

Step-by-step explanation:

We have been given that you save 3 ,260.00 in a savings account earning a 3.55% APR compounded monthly. We are asked to find the total interest earned by the end of the third month.

We will use compound interest formula to solve our given problem.

[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,

A = Amount of interest after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of periods interest is compounded per year,

t = Time in years.

[tex]3.55\%=\frac{3.55}{100}=0.0355[/tex]

[tex]\text{3 months}=\frac{3}{12}\text{ year}=\frac{1}{4}\text{ year}[/tex]

Upon substituting our given values in above formula, we will get:

[tex]A=3,260(1+\frac{0.0355}{12})^{12\times \frac{1}{4}}[/tex]

[tex]A=3,260(1+0.002958333)^{3}[/tex]

[tex]A=3,260(1.002958333)^{3}[/tex]

[tex]A=3,260*1.00890128109888[/tex]

[tex]A=3289.0181763823\approx 3289.02[/tex]

Now, we will subtract principal amount from final amount to find amount of interest.

[tex]\text{Amount of interest}=3289.02-3260[/tex]

[tex]\text{Amount of interest}=29.02[/tex]

Therefore, you will earn am amount of $29.02 by the end of the third month.

Answer: that would be 112 oz

Step-by-step explanation:

Answer:

I believe the correct answer is  112 Ounces

Step-by-step explanation:

: 16 (1 lb = 16 oz)

which means you would do 7 times 16

108 is the number of blueberry baglels

∠R = ∠Q, AS = AT       Given

∠5 = ∠6                        Base ∠'s of isosceles triangle are =

∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary           Exterior sides in opposite rays

∠4 = ∠7                         Two ∠'s supplementary to equal ∠'s are =

Triangle RAS congruent to Triangle QAT          AAS

RS = QT                          CPCTE

Answer:

∠R = ∠Q, AS = AT       Given

∠5 = ∠6                        Base ∠'s of isosceles triangle are =

∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary           Exterior sides in opposite rays

∠4 = ∠7                         Two ∠'s supplementary to equal ∠'s are =

Triangle RAS congruent to Triangle QAT          AAS

RS = QT                          CPCTE

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

as long as the polygon is not dilated or the size of the polygon is not changed in any way, the area should stay the same.

(5,3)

1. Determine the rule for this rotation

(x,y) ---> (-y,x)

2. Plug in

(3, -5) ----> (5,3)

Answer

(5,3)

Answer:

( -5, -3) .

Step-by-step explanation:

Given : A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5).

To find : what are the coordinates of its image point.

Solution : We have given that

Parent coordinates (3, -5)

If the  point is rotated 90° clockwise.

By the rotation rule of 90° clockwise (x ,y) →→ ( y , -x) .

Then  (3 ,-5) →→ ( -5, -3)

Therefore, ( -5, -3) .

Answer:

5270cm^2

Step-by-step explanation:

85 * 62 = 5270

It says it is asking for square centimeters and area, so use the formula for the area of a rectangle (b * h).

Answer: 5270cm^2

Step-by-step explanation: 85 * 62 = 5270

Answer:

3 pallets

Step-by-step explanation:

Divide to find the amount of pallets:

Subtract Exponents to divide

15^13 / 15^5 = 13 - 5 = 8 - 5 = 4 (subtracted 2 times)

You need three to store ALL the water

The stock room will need [tex]15^8[/tex] pallets to store the received [tex]15^13[/tex] water bottles since each pallet can store [tex]15^5[/tex] water bottles and we divide the total number by the pallet capacity.

To calculate the number of pallets needed to store all the water bottles the stock room received, we need to divide the total number of water bottles by the number of bottles a single pallet can hold.

The pallet can store 155 water bottles, and the stock room receives 1513 water bottles. By dividing the total number of bottles by the capacity of a pallet, the calculation is:

1513 ÷ 155 = 1513-5 = 158

Therefore, the stock room will need 158 pallets to store all the received water bottles.

Answer:

the answer is

The surface area of Figure 1 is 10.2 square centimeters Less than the surface area of Figure 2.

Step-by-step explanation:

Figure 1

area of a square = s2

=9squared

=81 sq cm

area of triangle = 1/2 bh

=1/2 (9cm) (14cm)

=63 sq. cm

find surface area

SA = 81 sq. cm + 4(63 sq. cm)

SA = 81 sq. cm + 252 sq. cm

SA = 333 sq. cm

Figure 2 Calculation

area of rectangle = lw

a = (12cm) (8 cm)

a = 96 sq. cm

area of triangle = 1/2 bh

=1/2 (8 cm) (6.9 cm)

= 27.6 sq. cm

total surface are of figure 2

SA = 3 (96 sq.cm) + 2 (27.6 sq. cm)

SA = 288 sq. cm + 55.2 sq. cm

SA = 343.2 sq. cm

find the difference between figure 1 and figure 2

343.2 sq. cm - 333 sq. cm = 10.2 sq. cm

Final answer:

We cannot complete the statement definitively about the surface area comparison between the square pyramid and the triangular prism without specific measurements. However, if we knew the dimensions, we could use the principle that surface area scales with the square of the linear dimensions to compare the two.

Explanation:

To complete the statement about the surface areas of Figure 1 (a square pyramid) and Figure 2 (a right triangular prism), we need to consider how areas scale with the dimensions of the shapes. Salviati's example illustrates that surface areas scale with the square of the linear dimensions, which is an important concept in geometry. Applying this concept to two triangles where one is larger than the other with linear dimensions twice as long, the larger triangle will have an area four times greater (area scales with the square of the linear dimensions).

Correct solution #1: Since the larger triangle's sides are twice as long, its area is 22 = 4 times more than the smaller triangle. If we applied similar reasoning and knew the dimensions of Figure 1 and Figure 2, we could compare their surface areas. However, with the provided information, we cannot definitively complete the given statement about the surface area of the pyramid relative to the prism without the specific measurements of each figure.

By understanding that the surface area of shapes scales with the square of their dimensions and using examples like cutting the larger triangle into four smaller ones (correct solution #2), we can tackle the surface area comparison confidently, provided we have the necessary dimensions.

Answer: 26in

s=r*theta

r=s/theta

d=r*2

136ft=r*40pi

r=136/40pi=1.082ft

d=1.082*2=2.1645ft*(12in/1ft)=25.97in

Rounded to nearest in is 26in diameter

The diameter of the bike's tire is calculated by dividing the total distance traveled by the number of revolutions to find the circumference and then dividing the circumference by pi (π) to find the diameter, which is approximately 26 inches.

To find the diameter of the bike’s tire, given that it completes 20 revolutions and travels 136 feet, we can use the relationship between the circumference of a circle (in this case, the tire) and its diameter.

First, we calculate the circumference of the tire by dividing the total distance traveled by the number of revolutions:

Circumference = Total Distance ÷ Number of Revolutions

Total Distance = 136 feet (1 foot = 12 inches, so convert feet to inches for precision)

Total Distance in inches = 136 feet × 12 inches/foot = 1632 inches

Circumference = 1632 inches ÷ 20 = 81.6 inches

Now, we use the circumference to find the diameter:

Circumference = π × Diameter

Diameter = Circumference ÷ π

Diameter ≈ 81.6 inches ÷ π ≈ 26 inches

Therefore, the diameter of the bike’s tire, rounded to the nearest inch, is approximately 26 inches.

Answer:

Chuck can afford both the convertible and sports car APEX

Step-by-step explanation:

Answer:

We can say that Chuck can afford both the cars.

Step-by-step explanation:

The EMI formula is :

[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

p = 28700

r = 6/12/100=0.005

n = 6*12=72

Putting the values in the above formula, we get:

[tex]\frac{28700*0.005*(1.005)^{72} }{(1.005)^{72}-1 }[/tex]

Monthly payment is = $475.67

p = 29200

r = 6/12/100=0.005

n = 6*12=72

Putting the values in the above formula, we get:

[tex]\frac{29200*0.005*(1.005)^{72} }{(1.005)^{72}-1 }[/tex]

Monthly payment is = $483.96

We can see that in both the cases, the monthly payments or EMI's are less than $490.

Therefore, we can say that Chuck can afford both the cars.

Answer:

it will be less than

Step-by-step explanation:

Answer:less than

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

with b = 4 and n = - 2

[tex]log_{4}[/tex] [tex]\frac{1}{16}[/tex] = - 2, then

[tex]\frac{1}{16}[/tex] = [tex]4^{-2}[/tex] ← in exponential form

ANSWER

The exponential form is

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

EXPLANATION

The given logarithm is

[tex] log_{4}( \frac{1}{16} ) = - 2[/tex]

We want to write the given logarithm in exponential form:

We take the antilogarithm of both sides to obtain:

[tex] {4}^{log_{4}( \frac{1}{16} )} = {4}^{ - 2} [/tex]

We simplify the left hand side to obtain:

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

Hence the exponential form is

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

7 Hours on Average

add up all the hours and you get 35

then divide 35 by the number of given hours which is 5

35/5 = 7

so the average amount of hours slept was 7

Answer:

7 hours

Step-by-step explanation:

To find this average, add up the five data points given and divide your result by five (5):

(7 + 9 + 5 + 6 + 8) / 5 = 35 / 5 = 7

This group of students averaged 7 hours of sleep per night.

After multiplying by the LCD, the denominators are eliminated, resulting in the equation (x-2)(x+2) - 3x = (x-2)(x-3). Further simplifying this equation, we obtain x^2 - 3x - 4 = x^2 - 5x + 6 which can then be solved with algebraic methods.

To solve the given equation by multiplying each term by the lowest common denominator (LCD), which is 3x(x-2), we need to eliminate the fractions first.

The given equation is:

(x+2)/(3x) - 1/(x-2) = (x-3)/(3x)

After multiplying each term in the equation by the LCD, we have:

Now, we can write the new equation without denominators:

(x-2)(x+2) - 3x = (x-2)(x-3)

Next, we simplify it:

x^2 + 2x - 2x - 4 - 3x = x^2 - 3x - 2x + 6

x^2 - 3x - 4 = x^2 - 5x + 6

This equation can now be simplified or solved using algebraic methods such as combining like terms or moving all terms to one side in preparation for factoring or applying the quadratic formula.

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Answer:

(x-2)(x+2) - 3x = (x-2)(x-3)

Step-by-step explanation:

Answer:

The answer .03 is 10 times greater than .003

Step-by-step explanation:

.003 x 10= .03

Final answer:

The value of 0.03 is ten times greater than the value of 0.003. This is evident by observing that 0.03 is expressed as 3 x 10^-2 while 0.003 is expressed as 3 x 10^-3, showing 0.03 is one decimal place to the left of 0.003.

Explanation:

The value of 0.03 is ten times greater than the value of 0.003. This conclusion is reached by observing the placement of the decimal point. For each power of ten we move to the right, the number becomes 1/10 the size of the previous number. Conversely, moving one place to the left (making the number ten times bigger), we increase the value of the number by a factor of 10.

Expressing these numbers with negative exponents, we have:

As illustrated above, since 10-3 is one factor of 10 smaller than 10-2, the value 0.03 is ten times greater than 0.003.

Answer:

View the picture please!

Step-by-step explanation:

Answer:

What did he have before?

Step-by-step explanation:

A is the correct answer

Answer:

Step-by-step explanation:

The graph has a relative minumum.  TRUE   Actually, I'd call it an absolute minimum, since 5 is the smallest y value and the graph opens up.

The graph shown has a vertex at (0, 5)  TRUE.  This point is also the absolute minimum of the function.

The graph opens up.  TRUE

The graph has neither one nor two x-intercepts.  The graph never crosses or touches the x-axis.  

Answer:

A,B,C,F

Step-by-step explanation:

everything above was right except that there were more answers! For Algebra Nation the photo is incomplete and doesnt show the last two questions. I just took the test

Set u a ratio of height over shadow:

Lance = 5 feet tall / 8 foot shadow

Tree = X feet tall / 32 foot shadow.

Set the ratios equal to each other and solve for X:

5/8 = x/32

Cross multiply:

8x = 160

Divide both sides by 8:

x = 160/8

x = 20

The tree is 20 feet tall.

For this case, I should find the unit cost per pound of orange.

[tex]\frac {4} {2} = 2 \frac {dollars} {libra}[/tex]

Zack wants to buy at the same price per pound.

Then, you can buy peaches:

[tex]\frac {6} {3} = 2 \frac {dollars} {pound}[/tex]

Answer:

Option C

Peaches at $ 6.00 for 3 pounds

Answer:

D) 4176 unit cubes

Step-by-step explanation:

Length of the right rectangular prism [tex]=7\frac{1}{4}[/tex] inches

Width of the right rectangular prism [tex]=8[/tex] inches

Height of the right rectangular prism [tex]=9[/tex] inches

Then volume of the right rectangular prism = (Length)(Width)(Height)

[tex]=\left(7\frac{1}{4}\right)\left(8\right)\left(9\right)[/tex]

[tex]=\left(7.25\right)\left(8\right)\left(9\right)[/tex]

[tex]=522[/tex] cubic inches

Now volume of the small cubic prism [tex]=(Length)^3=\left(\frac{1}{2}\right)^3=\frac{1}{8}[/tex]

Then number of cubes that can fit into the right rectangular prism [tex]=\frac{522}{\left(\frac{1}{8}\right)}=522*8=4176[/tex]

Hence correct choice is D) 4176 unit cubes

Answer:

M<FDE = 360 degrees

Step-by-step explanation:

120 degrees is supplementary to x which makes it 120. 120+120=240 degrees. angle x and angle d = 120+120 which makes it 360 degrees.

M<ADE however, is 110+120=280, 360-280=80 degrees which is 110+120+80=360 degrees. So, M<ADE is 360 degrees and it is equal to M<FDE which is also 360 degrees.

All of them are equal. The sum of the figure is 720 Degrees.

Answer:

∠FDE = 130°

Step-by-step explanation:

Since BC and DE are parallel lines, then

∠BDE = ∠ABC = 110° ( corresponding angles are congruent )

The sum of the angles round a point = 360°, thus

∠BDE + ∠BDF + ∠FDE = 360 , hence

110 + 120 + x = 360

230 + x = 360 ( subtract 230 from both sides )

x = 130

Hence x = ∠FDE = 130°

Answer:

c

Step-by-step explanation:

La raíz de la cuadra de 81 es 9

Answer:

the square root o 81 is 9

Step-by-step explanation:

9x9=81