5
Isabella wants to create 23 ounces of new hand lotion, with a minimum 15% concentration of beeswax, from a mixture of two lotions.
One lotion has a 21% concentration of beeswax, and the second lotion has a concentration of 5% beeswax. Based on the inequality
below, how much of the 21% lotion, x, will she need?
O A. x≥ 14.375
O B.
x2 15.33
OC.
x2 20.125
O D. x2 11.5
0.21x+0.05(23-x) ≥ 3.45

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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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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2a+b=15.7 is the formula used to get the base's length and b has a value of 3.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and Skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

An isosceles triangle has 2 equal sides that are longer than the length of the base

perimiter=15.7

equation is 2a+b=15.7

so if the longer side is 6.3

we know that identical sides are bigger so 6.3 is one of the identical sides

2a means the 2 identical sides

2(6.3) + b = 15.7

12.6 + b = 15.7

subtract 12.6 from both sides

b = 3.1

therefore, The equation used to find the length of the base is 2a+b=15.7

and the value of b is 3.1

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Answer:

12.6 + b = 15.7

Answer:2/5

Step-by-step explanation:

2/5+1/5 equals 3/5, so if the rest of the mixture is chili powder, it would be 2/5

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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The volume of air present in the room is 27410.7075 lt .

The space occupied inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to imagine in any shape, yet it may be compared amongst shapes. For instance, a compass box has a larger volume than an eraser placed inside of it. We split the area into equal square units to get the area of any two-dimensional form. Similar to this, we shall split the volume of solid objects into equal cubical units while calculating it. In the part after this one, let's examine how to determine the volume of various solid forms.

The dimension of the room is 11*11*8 in feet.

so, 11 ft = 11 *2.54*12 = 335.28 cm

And, 8 ft = 8 *2.54*12 = 243.84 cm

Volume of the room is = 335.28 * 335.28 * 243.84 = 27410707.5 [tex]cm\x^{3}[/tex]

In litre,

27410707.5 [tex]cm\x^{3}[/tex] = 27410707.5/1000 = 27410.7075 lt.

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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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The exponential function formula for the parent function is found to be

[tex]f(x) = 2^x[/tex]

What is an exponential function?

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The general formula to find an exponential function is [tex]f(x) = ab^x[/tex]

From the given graph, we take two points on the graph : (1,2) and (2,4)

Substituting in the above equation, taking f(x) as y

[tex]ab^1 = 2\\\\ab^2 = 4[/tex]

Solving the above equations, we get

a= 1, b=2

So the parent function  [tex]f(x) = 2^x[/tex].

Now using this function we can graph [tex]f(2x), -3f(x), 2f(2x)\\[/tex].

[tex]f(2x) = 2^{2x} = 4^x\\\\-3f(x) = -3 * 2^x\\2f(2x) = 2 * 4^x[/tex]

Therefore using the Desmos, the above exponential functions are graphed.

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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

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 horizontal distance required for the ramp is 143.5 inches

Consider the following figure.

In right triangle ACB, CB is the horizontal distance,

hypotenuse AB = 144 in.

and the vertical distance AC = 12 in.

We need to find the measure of side CB

Let m be the measure of the horizontal distance CB

Using Pythagoras theorem for right triangle ACB,

(AB)² = (AC)² + (CB)²

Substitute given values in above equation.

(144)² = (12)² + (m)²

20736 = 144 + m^2

20736 - 144 = 144 + m^2 - 144

20592 = m^2

m^2 = 20592

m = 143.5 in.

Therefore,  the horizontal distance is 143.5 in.

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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 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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Answer:

  more than 110

Step-by-step explanation:

You want to know the number of $6 tickets that must be sold to pay for the $660 cost of a school play and make a profit.

The profit is the difference between revenue and cost. The revenue from the sale of n tickets will be 6n. We want the profit to be positive, so we want ...

  6n -660 > 0 . . . . . . positive profit

  n -110 > 0 . . . . . . divide by 6

  n > 110 . . . . . . add 110

More than 110 tickets must be sold to make a profit.

__

Additional comment

Sale of exactly 110 tickets will cover the cost, but there will be no profit.

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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x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement  best describes the end behavior.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

First, we need to analyze the plotting of the graph. When it is on the negative axis of x, as the values of x increase (x values increasing in the negative axis means it's decreasing in value), the y values also increase. So as x decreases, y increases.

On the positive axis of x, as the x values increase, the corresponding values of y also increase with x. So as x increases, y values also increase with it.

Hence, x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this  statement  best describes the end behavior.

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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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The x-intercept of the line 4x-y =- 4  is (1,0).

At x-intercepts, y=0  and at

y-intercepts, x=0.

So, to find the,

x-intercept, set y=0

4x−0=4

4x=4

x=1.

The points at which the graph of a function or an equation crosses or "touches" the x-axis of the Cartesian Plane are referred to as the x-intercepts. This could be thought of as a point with a y-value of zero. Let y equal 0 and then solve for x to determine the equation's x-intercepts.

Because the line crosses the x-axis when y=0, the equation for x must be solved in order to determine the x-intercept. We can solve for the intercepts when an equation is not in the form y = mx + b by solving for the remaining variable and plugging in 0 as necessary. To locate the y-intercept: solve for y and set x to zero.

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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

Answer:

It will either invert the graph or stretch/compress the horizontal

Step-by-step explanation:

When a is negative It will invert the graph, and reflect it over the x-axis

By plugging in a=1 you get a normal absolute value function of x ( a V on the graph)

If a>1 then your graph will compress

If a<1 then your graph will stretch

∠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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The score of Larry is 32 points.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Ervin scores half as many points in a game as Larry.

If Larry scored x points,

then the points of Ervin are x/2 points.

Here, x = 16,

So,

Ervin's points = Larry's points

The equation is,

16 = x/2

x = 16(2)

x = 32 points

Therefore, 32 points are the score of Larry.

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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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The brand-name television's measurements are 32 inches by 64 inches, so answer (C) is accurate.

Given: The generic version was created based on the brand name and was three eighths the size of the brand name.

12 inches by 24 inches is the size of the standard television set.

Allowing for x by y as the brand name's measurements

12 inches divided by three eighths

8/3 x = 12

x = 12 * 8 / 3 = 32 inch

and y=3/8 inches equals 24 inches

8/3 y = 24

y = 24 * 8 / 3 = 64 inch

As a result, the brand-name television has the following measurements: 32 by 64 inches.

Therefore, choice (C) is the appropriate response.

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The complete question is: Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was  the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television?

a) 7.5 inches by 15 inches

b) 28 inches by 56 inches

c) 32 inches by 64 inches

d) 4.5 inches by 9 inches

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 )

By dividing we can get proper fraction is 9/10.We can find answer by dividing two fractions.

A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.. We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.

To divide a fraction with a whole number  we multiply the given whole number with the denominator of the fraction. Here, 8/5 ÷ 5 = 8/5 × 1/5 = 8/25. Therefore, 8/5 ÷ 5 = 8/25. Because multiplication is easier than division and because division by itself does not always produce whole numbers.

Now we get

1/2 divide 5/9

1/2 * 9/5

9/5

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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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The Geometric Mean (GM) is the average value or mean that, in mathematics, represents the centre tendency of a group of numbers by calculating the product of their values.

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).

The geometric mean of 14 and 20 must be determined. Let's see the numbers:

a = 14 and b = 20

For two numbers, the geometric mean is calculated as follows:

[tex]$M=\sqrt{a b}$[/tex]

Filling in the values as shown in the formula above:

[tex]$M=\sqrt{14 \times 20}$$M=\sqrt{7 \times 2 \times 5 \times 4}$$M=16.73$[/tex]

Therefore, the answer is 16.73.

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The required geometric mean of 14 and 20 is 16.73.

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).

The geometric mean of 14 and 20 must be determined. Let's see the numbers:

a = 14 and b = 20

For two numbers, the geometric mean is calculated as follows:

G.M = [tex]\sqrt{ab}[/tex]

Filling in the values as shown in the formula above:

G.M = [tex]\sqrt{14(20)}[/tex]

G.M = [tex]\sqrt{280}[/tex]

Therefore, the answer is 16.73.

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