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The minimum and maximum possible heights of the bowling pin are 14.96875 inches  and 15.03125 inches

From the question, we have the following parameters that can be used in our computation:

Absolute deviation = 0.03125 inches

Height = 15 inches

The minimum is calculated as

Minimum = Height - Absolute deviation

Substitute the known values in the above equation, so, we have the following representation

Minimum = 15 - 0.03125 inches

Minimum = 14.96875 inches

The maximum is calculated as

Maximum = Height + Absolute deviation

Substitute the known values in the above equation, so, we have the following representation

Maximum = 15 + 0.03125 inches

Minimum = 15.03125 inches

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The measure of angle B is 107°.

What do similar triangles mean?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given a triangle, NPZ is similar to triangle HBZ.

Which can also be written as ΔNPZ ≈ ΔHBZ

So, by equating the corresponding angles that are angle P = angle B:

8x-37°=180-(2x-5+42)°

10x=180

x=18°

So, H=36-5=31°

Since the sum of all angles in a triangle is 180°, angle B can be calculated  as

B= 180°-(42+31)°

B=107°

Therefore the measure of angle B is 107 degrees

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Answer: Perimeters Are Shown Below

Step-by-step explanation:

6. 2 Hexagons; 1+1+1+1+1+1+1+1+1+1   OR 1 x 10

6. 3 Hexagons; 1+1+1+1+1+1+1+1+1+1+1+1+1+1  OR 1 x 14

7. 2 Pentagons; 1+1+1+1+1+1+1+1  OR 1 x 8

7. 3 Pentagons; 1+1+1+1+1+1+1+1+1+1+1  OR 1 x 11

The ratio of yellow paint to mixed paint is 3/5.

A ratio is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is written as a/b or a: b. An equality of two ratios is a proportion. In order to write equivalent ratios, proportions are used, which aids in resolving the unknown quantities. As an illustration, a proportion is written as a: b = c: d.

Solution:-

Given,

Amount of yellow paint=3

Amount of blue paint=2

Ratio=yellow paint/total mixed paint

Ratio=3/(3+2)

Ratio=3/5

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Answer:

-15

Step-by-step explanation:

That's the answer because

-15+4=-11

-15+4=-11-11<-7

Call the radius of the cylinder and sphere, r And the height  of the cylinder  = 2r

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The total area of the two rectangles is given by the equation A = 33 units²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the total area of the 2 rectangles be A

Now , each grid square represents = 1 square unit

Now , let the first rectangle be represented as P

The length of P = 4 grid squares

The width of P = 3 grid squares

Let the second rectangle be represented as Q

The length of Q = 7 grid squares

The width of Q = 3 grid squares

So , Area of Rectangle = Length x Width

The area of rectangle P = 4 x 3

The area of rectangle P = 12 units²

The area of rectangle Q = 7 x 3

The area of rectangle Q = 21 units²

So , the total area of figure A = area of P + area of Q

On simplifying the equation , we get

Total area of figure A = 12 units² + 21 units²

Total area of figure A = 33 units²

Therefore , the value of A is 33 units²

Hence , the area is 33 units²

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By standard deviation, 68% housing price are between a low price of $135000 and a high price of $149000.

What is standard deviation in math?

The variability in your dataset is measured by its standard deviation. It reveals the average deviation between each result and the mean.

                           A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.

Given,

         mean (μ) = 142000

  standard deviation (σ ) = 7000

 By using empirial rule,

                    P( μ - σ ≤ X ≤ μ + σ ) ≈ 68%

   Then,

             P(142000 - 7000 ≤ x ≤ 142000 + 7000 ) ≅ 68%

    P( 135000 ≤ x ≤ 149000 ) ≅ 68%

68% housing price are between a low price of $135000 and a high price of $149000.

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The length of other base  is 15 cm.

The area of a trapezoid can be found by using the formula:

Area = (b1+b2) * h / 2 where b1 and b2 are the lengths of the bases, and h is the height.

Given that the area of the trapezoid is 135 cm^2, the height is 10 cm, and one base is 12 cm, we can substitute these values into the formula to find the length of the other base.

Area = (b1+b2) * h / 2 = 135cm^2

We can solve for the other base length by isolating b1

b1 = 2*Area/h - b2

b1 = 2*135/10 - 12 = 27 - 12 = 15

So, the other base length is 15 cm.

Therefore, The length of other base  is 15 cm.

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2 is not a polynomial root of  [tex]x^{3} + 4x^{2} + 3x[/tex] . A polynomial is an equation that employs addition, subtraction .

A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients that uses solely the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that employs addition, subtraction, multiplication, and division of numbers to combine variables, constants, and exponents (No division operation by a variable).

given

[tex]x^{3} + 4x^{2} + 3x[/tex]

= [tex]2^{3} + 2^{2} + 3(2) = 0\\8 + 4 + 6 = 0 \\18= 0[/tex]

Consequently, 2 is not a polynomial root of  [tex]x^{3} + 4x^{2} + 3x[/tex] .

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Answer:

f(6) = - 50

Step-by-step explanation:

substitute x = 6 into f(x) , that is

f(6) = - 6² - 14 = - 36 - 14 = - 50

Answer:

-50

Step-by-step explanation:

f ( x ) = - x² - 14

Accordingly, to find the value of f ( 6 ) you have to replace x with ( 6 ).

f ( 6 ) = - (6)² - 14

f ( 6 ) = - 36 - 14

f ( 6 ) = -50

The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: A card is drawn from a standard deck of 52 cards. Let the probability be P then P= 1/52

                                     =0.02

Hence, The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)

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When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.

The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

Let x be the price of a single tulip bag.

Y should equal the price of one bag of daffodil bulbs.

Grace = 14x + 12y = 254

ava = 6x + 12y = 198

- 8x = - 56

x = - 56/-8

x = 7.

Equation 1 becomes

6* 7 + 12y = 198

42 + 12y = 198 when x = 7 is substituted.

12y = 198 - 42

12y = 156

y = 156/12

y = 13

When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.

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A particle traveled a distance of 9.0×10¹² meters in 5.0 × 10⁷ seconds.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

If a particle traveled a distance of 9.0×10¹² meters at a rate of 1.8×10⁵meters per second.

And the distance,

= rate x time.

Rearranging the formula,

Time = Distance / rate

Time = 9.0×10¹² / 1.8×10⁵

Simplifying by using division operation,

Time = (9.0/1.8) × 10¹² × 10⁻⁵

Time = 5.0 × 10⁷

Therefore, the required specified time is  5.0 × 10⁷ seconds.

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The algebraic expression for the given sequence 1, 10, 19 as required to be determined is; a (n) = 1 + ( n - 1 ) 9.

As evident in the task content; it follows that the common difference of the given sequence is constant since; 19 - 10 = 10 - 1 = 9.

On this note, since the nth term of arithmetic sequences take the form;

a (n) = a (1) + ( n - 1 )d

Since the first term is; 1 and the common difference is; 9; the resulting algebraic expression is;

a (n) = 1 + (n - 1)9.

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Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.

A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.

5 : This is the number of baseball players who are in 8th-grade

73: This is the total of players. You get this number if you add all the numbers given.

Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".

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The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

The given expression:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

To find the formula for K

The formula for K is obtained by making K the subject of the formula as shown below:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

subtract 32 from LHS.

[tex]F-32 = \frac{9}{5} (K-273)[/tex]

multiply 5 with LHS

[tex]5(F-32) = 9(K-273)[/tex]

Take numerator 9 to LHS

[tex]\frac{5}{9}(F-32) = K-273[/tex]

take -273 from RHS to LHS

[tex]\frac{5}{9}(F-32) + 273 = K[/tex]

Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

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Therefore, As a result, the answer to the given equation problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.

Define equation .

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.

Here,

The formula is: 1/j +1/j+ 21 = 11/ 4.

LCM = j+21+j / j(j+21)=1/14

Thus, 2j+21 / j(j+21) = 1/14 is obtained.

14(2j+21) times itself yields j(j+21).

28j+294 expanded to j²+21j

Gather comparable terms

j²+21j-28j-294=0

j²- 7j-294=0

With the use of a graphing calculator, we have:

j = 21 or j= -14

Due to the context,

j's value cannot be negative.

As a result, the answer to the given equation's problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.

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"If p then q" is a conditional statement, and its contrapositive is If ~q then ~p.

Knowing about the inverse statement makes it simple to comprehend how to build a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite.

Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement. Adding "not" to both component statements and switching the order of the provided conditional statements will result in contrapositive assertions, in other words.

If a number n is even, then n2 is even, and vice versa, is the contrapositive statement to "If a number n is even, then n2 is even."

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Answer:

Step-by-step explanation:

Perimeter is the addition of all the sides.

So in this question, if you add up all the sides :

14x + 8x +7x +12

Simplify by adding all terms with x :

29x + 12  

(As you can not add a number constant to a variable )

Answer:

a) 4.2 - 2.8 = 1.4

b) 72.1 - 45.6 = 26.5

c) 82.2 - 41.3 - 29.2 = 11.7

d) 17.1 - 11.7 - 0.8 = 4.6

e) 29.2 - 12.5 - 0.9 = 15.8

f) 21 - 14 = 7

g) 71 - 37 - 18 = 16

h) 50 - 19 - 8 = 23

i) 92 - 57 - 16 = 19

j) 44 - 18 - 9 = 17

The expected number of ball pens of a student is 2.4.

What is the expected number?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.

The weight for each group is the percentage of students that are in that group.

So, we can calculate the expected number of ball pens of a student by:

(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)

0.7 + 0.9 + 0.8 + 0.2

The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.

Here, the outcome is the number of ball pens.

Hence, the expected number of ball pens of a student is 2.4.

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To fill one urn with one white ball and the second urn with the remaining nine white and ten black balls.

Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.

The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or P(A) = f/N

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∠DAC = 28°

∠BAC = 56°

PL = 20

BD =​ 31

Bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

An angle bisector divides an angle into equal angles. If the angle is p°, the two angles made will be (p/2)°. This angle bisector passes through the vertex of an angle.

Example: Consider an Angle ∠ABC = 90°. An angle bisector will cut it into two equal angles of 45° each.

Given, AD bisects ∠BAC

MP = 20

DC = 31

∠BAD = 28°

AD bisects ∠BAC

⇒ ∠BAD = ∠DAC

⇒ ∠DAC = 28°

∠BAC = ∠BAD + ∠DAC

∠BAC = 28° + 28°

∠BAC = 56°

Since, In a figure, sides opposite to the equal angles are also equal

∠BAD = ∠DAC

⇒ BD = DC

⇒ BD = 31

⇒ BD = 31

By the figure,

∠MAP = ∠BAD and ∠PAL = ∠DAC

⇒ ∠MAP = ∠PAL

⇒ MP = PL

⇒ PL = 20

Hence, by the above calculation the measure of ∠DAC = 28°,

∠BAC = 56°, PL = 20, BD = 31.

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We can find the x-intercept by writing the equation in intercept form which  is also known as factored form, y= (x-p) (x-q) where p, q are the x-intercepts.

To find the vertex of the quadratic function we can write the function  in standard form , the vertex is located at the point where y=f (x).

A function which has a degree of two is known as a quadratic function.

Example, 3x² + 2 , here the maximum degree is 2 , hence the given function is quadratic. The general form of a quadratic equation is given as ,

f(x) = ax2 + bx + c .

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Answer:

5,775 for the cost of parking tuition

Step-by-step explanation:

45% = 0.45

0.45(10,500)= 4,725

10,500 - 4,725 = 5,775 for the cost of parking tuition

The equation of the linear function after a translation down 9 units is given as follows:

f(x) = x - 11.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph of the function crosses the y-axis at y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 2 units, from x = 0 to x = 2, y increases by 2 units, from y = -2 to y = 0, hence the slope is calculated as follows:

m = 2/2.

Then the function is of:

y = x - 2.

After the translation down 9 units, 9 is subtracted from the function, hence:

f(x) = x - 2 - 9

f(x) = x - 11.

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The fraction after solving and simplifying the mixed fraction 5 3/4 ÷ 1 1/2​ is 23 / 6.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. For instance, 8 1 / 2 is a mixed fraction if 8 is a whole number and 1/2 is a fraction.

Given:

5 3/4 ÷ 1 1/2​

Solve the mixed fraction into improper fractions as shown below,

5 × 4 + 3 / 4 ÷ 1 × 2 + 1 / 2

20 + 3 / 4 ÷ 2 + 1 / 2

23 / 4 ÷ 3 / 2

23 / 4 × 2 / 3

23 × 2 / 4 × 3

On simplifying,  

23 × 1 / 2 × 3

23 / 6

Thus, the value is 23 / 6.

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Answer:

There might be an error in the question, the result below should be the correct answer. It is not possible for a^2+b^2+c^2 to be the answer.

(a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2

Step-by-step explanation:

(a+b+c)(a-b+c) = a^2 - ab +ac + ba - b^2 +bc + ca - cb + c^2 (expanding the two terms in brackets first)

Since ab = ba, ac = ca and bc = cb,

-ab and ba can be cancelled out

bc and -cb can be cancelled out

Hence, (a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2

This is what I have obtained through expansion, then simplification by cancelling out the common terms.

Could you help check the question again?