Evaluate 3|12−x|−4 when x=15

The measure of the longer diagonal is 24.31 units

The side lengths are given as;

a = 16

b = 10

The shorter diagonal is represented as d1, and it is given as

d1 = 11

The longer diagonal is represented as d2, and it is calculated using

d1^2 + d2^2 = 2 * (a^2 + b^2)

Substitute the known values in the above equation

11^2 + d2^2 = 2 * (16^2 + 10^2)

Evaluate the sum

121 + d2^2 =2 * 356

Evaluate the product

121 + d2^2 = 712

Subtract 121 from both sides

d2^2 = 591

Take the square root of both sides

d2 = 24.31

Hence, the measure of the longer diagonal is 24.31 units

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Answer:

C (third figure from left)

Step-by-step explanation:

The spirals in the first, second, and fourth figures are all clockwise from the outer end, i.e., if you trace these three spirals with your finger from the outside to the inside, your finger will move clockwise.

However, if you did the same with the third figure, you would see that the spiral is anti-clockwise from the outside moving in.

Therefore, the third figure doesn't belong.

Answer:

x² + 6x + 9

Step-by-step explanation:

(x + 3)²

= (x + 3)(x + 3)

each term in the second factor is multiplied by each term in the first factor , that is

x(x + 3) + 3(x + 3) ← distribute parenthesis

= x² + 3x + 3x + 9 ← collect like terms

= x² + 6x + 9 ← in standard form

The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

In 5-card poker, find the probability of being dealt the following hand. Refer to the table.

From the table:

Total number of outcomes = 2598960

Total number of favorable outcomes = 624 + 10200 = 10824

The probability of being dealt four of a kind or a straight

P = 10824/2598960

P = 0.00416

In percentage:

P = 0.416%

Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.

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Answer:

(A)81/399

Step-by-step explanation:

The probability that the Principal selects a voyager on the first try is

82/400

Since another student is to be selected, the total population has reduced by 1 and the number of voyagers has been reduced by 1.

Probability that another voyager is selected on the second try is

81/399

The correct answer is A.

If the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.

The measures of central tendency include the mode, the median, and the mean.

Statistically, a central tendency is a typical value for a probability distribution.

The mode's value appears most often in a set of data values.  The median is the middle value of a dataset.  The mean represents the average.

To determine the possible values of A and B, we can start by finding the median value, which is the middle value in ascending order.

Median (Middle value) = 8

Mode = 8

Total value = 40 (8 x 5)

A = 8

B = 12.

Mean = 8 (40/5)

Thus, if the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.

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Answer:

angle G

Step-by-step explanation:

the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G

Answer:

2

Step-by-step explanation:

Using a line of best fit, the predicted tsunami speed for the following depths is given by:

a. 1151 km/h.

b. 572 km/h.

c. 130 km/h.

d. 122 km/h.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (depth, velocity) are given by:

(7000, 943), (4000, 713), (2000, 504), (200, 159), (50, 79), (10,36)

Inserting these points in the calculator, the velocity in function of the depth is:

v(d) = 0.12879d + 121.03448

Hence, the velocities are given as follows:

a. v(8000) = 0.12879 x 8000 + 121.03448 = 1151 km/h.

b. v(3500) = 0.12879 x 3500 + 121.03448 = 572 km/h.

c. v(70) = 0.12879 x 70 + 121.03448 = 130 km/h.

d. v(5) = 0.12879 x 5 + 121.03448 = 122 km/h.

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Answer:

None of these answers are correct.

Step-by-step explanation:

[tex]QR=\frac{25+45}{2}=35[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

By Trapezoid mid - segment theorem :

[tex] \qquad❖ \: \sf \:QR = \cfrac{MN+ OP}{2} [/tex]

[tex] \qquad❖ \: \sf \:QR= \cfrac{25+ 45}{2} [/tex]

[tex] \qquad❖ \: \sf \:QR = \cfrac{70}{2} [/tex]

[tex] \qquad❖ \: \sf \:QR= 35 \: \: units[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

2/7 = 29% (nearest percent)

Step-by-step explanation:

Calculate the totals and add them to the table:

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}[/tex]

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student is male

Use the given table to calculate the probability that the student is male:

[tex]\sf \implies P(B)=\dfrac{14}{30}[/tex]

And the probability that the student is a freshman and male:

[tex]\implies \sf P(A \cap B)=\dfrac{4}{30}[/tex]

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

[tex]\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%[/tex]

Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).

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Answer: 2

Step-by-step explanation:

When a^b = c, loga(c) = b

So b^5 = 32 and b is 2

Step-by-step explanation:

there are

1 red marble

3 blue marbles

4 green marbles

in the box.

that means there are 8 marbles in the box. which gives us 8 different outcomes for pulling randomly 1 marbles.

the probability for each of these 8 outcomes is equal : 1/8.

remember, the probability is always the number of desired cases over the number of total possible cases.

so, the probability of pulling a red marble is :

1 desired case

8 total cases

->

1/8 or 0.125

the probability of pulling a blue marble is :

3 desired cases

8 total cases

->

3/8 or 0.375

the probability of pulling a green marble is :

4 desired cases

8 total cases

->

4/8 = 1/2 or 0.5

now the experiment is pulling 2 marbles in a row, but the first pulled marble is put back into the box again.

this makes this a combined event, where the first AND the second event must fulfill the desired over total cases.

if the 2 events are independent (not overlapping or influencing each other), then we can simply multiply the probabilities. which is the case here, because the first marble is put back.

why ?

because now we have 8 possible outcomes for the first ball, and again 8 possible outcomes for the second ball, and when we combine all possibilities from the first with all possibilities from the second pull, we get 8×8 = 64 possible outcomes :

red. red

red. blue1

red. blue2

red. blue3

red. green1

...

green4 green4

so, the probability to pull a blue ball first is

3/8

and the probability to pull a blue ball second is

3/8 too

the combined probability of the combined event is

3/8 × 3/8 = 9/64

we have 3×3 = 9 desired outcomes of combining 3 blue and 3 blue balls out of the total of 64 possible outcomes.

The length of segment A.F in the circles given is: 62 units.

A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.

Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].

Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].

CD = 4

DE = x

CD + DE = CE

Plug in the values into the equation

4 + x = 9

x = 9 - 4

x = 5

DE = 5

The length of segment DE is 5 units

A.F = AB + BD + DE + EF

Plug in the values into the equation

A.F = 24 + 24 + 5 + 9

A.F = 62 units.

Therefore, the length of segment A.F in the given circle is determined as: 62 units.

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The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is

[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]

The percentage yield of carbonic acid is 66 percent.

The percentage yield of the  carbonic acid  can be found as follows:

NaHCO₃  →  Na₂CO₃  +  H₂CO₃

Hence, 2.36g sample of NaHCO₃ was thermally decomposed to generate 1.57g of carbonic acid (H₂CO₃)

Using law on conservation, the mass of the reactant is equals to the product.

Therefore,

percentage yield of carbonic acid = 1.57 / 2.36 × 100

percentage yield of carbonic acid = 157 / 2.36

percentage yield of carbonic acid = 66.2447257384

percentage yield of carbonic acid = 66 %

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Answer:

$580

Step-by-step explanation:

{371x(100-34)/100}+371=580

The original price (rounded to the nearest dollar) is $497.

In this problem, we need to identify what's the original price of the new mattress.

Since we know that the sale price is $371 and is 34% lesser than the original price, we need to add 371 and 34%.

Grab a calculator and add 371 and 34%

we get:

371 + 34% = 497.14

Now round it to the nearest whole number, we get: 497

This is how the answer gets 497.

Hope this helps :)

The statements that applies are;

The property of power function is known to be peculiar to the field of math. A power function is known to be one that is made up of a variable base that tends to be raised to a fixed power.

Note that the function is one that is made up of a constant base that is often raised to a variable power.

Following the property of power function, we can be able to obtain the information above.

Therefore, The statements that applies are;

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6.665 grams of the 13 grams remain after 8 hours.

The decay equation for the 13 grams of iron-52 is:

[tex]N(t) = 13g*e^{(-ln(2)/8.3h)*t}}[/tex]

Where N is the amount of iron-52, and t is the time in years.

Where we used the fact that the half-life is exactly 8.3 hours.

Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:

[tex]N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g[/tex]

So 6.665 grams of the 13 grams remain after 8 hours.

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Answer:

  (b)  (x -10)(x +10)

Step-by-step explanation:

The factorization of the difference of squares is a special form:

  a² -b² = (a -b)(a +b)

Your expression is recognizable as the difference of squares:

  x² -100 = x -10²

Using the above form, the factorization is ...

  = (x -10)(x +10) . . . . . . . . matches the second choice

The required rewritten equation in terms of variable 'r' is r = -u/s²t. By applying simple arithmetic operations, the required equation is obtained.

Consider an equation c = ax + by. Solving for variable 'a'.  

Step1: Write the required variable terms on one side

Step2: Add/Subtract like terms if any or take common if any

Step3: Divide/Multiply the coefficient of the required variable

Step4: simplify the obtained terms for the required variable

As follows:

c = ax + by

⇒ ax = by - c

⇒ ax/x = (by - c)/x

∴ a = (by - c)/x

The given equation is u = -s²rt

dividing by 't' on both sides:

⇒ u/t = -s²rt/t

⇒ u/t = -s²r

dividing by 's²' on both sides:

⇒ u/s²t = -s²r/s²

⇒ u/s²t = -r

∴ r = -u/s²t

Thus, the required equation for variable 'r' is r = -u/s²t.

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July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

This is further explained below.

Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.

The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...

In conclusion, for the following data  July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

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Answer:

it's simple, put the values in the equation.

5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)

= 5 + 4( -9-8)

= 5+ 4 × -17

= 5-68 = -63 ans.

Answer:

5

Step-by-step explanation:

46/9.2 = 5

The volume of a container shows the amount of space that it has inside of it.

The use of bento boxes that has edges that are a foot long and the use of a rectangular-shaped container to ship it would have been more useful if the dimensions were provided.

Provided that the dimensions are provided, the formula that can be used to find the volume of a container is:

V = L × W × H

Where:

L= Length

W= Width

H= Height

It is worthy to note that your question is incomplete as you did not include the answer choices for how the manager found the volume of the container and other questions so a general overview was given.

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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21 bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total number​of bento boxes in the container.

The volume of the cord of wood will be similar to the volume of a rectangular prism. Then the correct option is C.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

The rectangular prism is the most typical geometric form used to approximate the volume of a cord of wood.

The wood is evenly cut into identical lengths, and when stacked, it forms a rectangular prism.

Therefore, C. rectangular prism is the right response.

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The image of X after the dilation is (a) (4, 0)

From the figure, the coordinates of X are given as:

X = (4, 0)

The dilation is given as:

Do,1

This means that we dilate X across the origin by a scale factor of 1.

So, we have:

X' = 1 * (4 - 0, 0 - 0)

Evaluate

X' = (4, 0)

Hence, the image of X after the dilation is (a) (4, 0)

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