Complete the steps to solve the equation 3x + 11 = 29.

Answer:

look at the photo..........

Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.

The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.

Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.

In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.

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The proper notation for each parts of the circle are:

A. point F B. segment CB C. Secant AB D. Tangent BD E. segment AB F. point B G. segment AE.

The radius of a circle represents the distance from the center to any point on its boundary, while a secant is a line that intersects the circle at two separate points.

A tangent is a line that makes contact with the circle at a single point, called the point of tangency.

Thus, we have:

A. Center of the small circle is: F

B. The radius of the large circle that is not part of a diameter is: CB

C. A Secant is: AB

D. A common Tangent is: BD

E. One chord from the large circle is: AB

F. A Point of Tangency = point B

G. Diameter of the large circle is: AE

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The property that justifies this statement is the Symmetric Property of Congruence.

The symmetric property of congruence states that If an angle is congruent to another angle, then the second angle is also congruent to the first angle.

A congruent geometric shapes are shapes having the same size and shape, or matching in size and shape and their corresponding angles are equal to each other.

If shape A is congruent to shape B and A= B , then B = A

Similarly,

If angle DEF is equal to angle HJK, then with the law of symmetry property of angle HJk is equal to angle DEF.

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The measure of angles inside the rhombus are:

∠1 = 56

∠2 = 56

∠3 = 34

∠4 = 34

We have,

In a rhombus,

The opposite angle is congruent.

So,

(56 + 56) = ∠1 + ∠2

And,

∠1 and ∠2 are equal angles.

So,

112 = 2∠1

∠1 = 56

∠2 = 56

Now,

All four angles in side the rhombus = 360

112 + 112 + ∠x + ∠x = 360

2∠x = 360 - 224

2∠x = 136

∠x = 68

This ∠x is the angle inside the rhombus.

And, ∠x/2 = ∠3 = ∠4

So,

∠3 = 68/2 = 34

∠4 = 34

Thus,

The measure of angles inside the rhombus are:

∠1 = 56

∠2 = 56

∠3 = 34

∠4 = 34

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lol ur from trms

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

Direct variation is of the form

y = kx

where k is a constant

Using the first set of point

9 = 5k

Divide by 5

9/5 = k

The equation becomes

y = 9/5 x

Using the second set of points

3 = 9/5 x

Multiply each side by 5/9

5/9 * 3 = 9/5 *5/9x

5/3 =x

If we divide the circle into 12 equal parts, each sector would have an angle of π/12 radians. By using the formula, we can calculate that the area of one sector would be (2π/3) square units.

To find the area of a sector, you can use the formula A = (θ/2) * r^2, where θ is the angle in radians and r is the radius.

To give you an example, let's say we have a circle with a radius of 4 units. In this case, the given angle is 0 = π/12 radians and the radius is 4. Let's substitute these values into the formula:

A = (π/12 / 2) * 4^2

Simplifying the expression inside the parentheses:

A = (π/24) * 16

Now, we can simplify further:

A = (π/24) * 16
A = (π/3) * 2
A = (2π/3)

Therefore, the area of the sector is (2π/3) square units.

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The probability that the selected pencil is red is 1/5

The distribution of the pencils are given as:

Red = 3

Green = 4

Black = 2

Blue = 6

When a pencil is selected, the probability that the pencil is red is:

P(Red) = Red/Total

This gives

P(Red) = 3/(3 + 4 + 2 + 6)

Evaluate the sum

P(Red) = 3/15

Simplify the quotient

P(Red) = 1/5

Hence, the probability that the selected pencil is red is 1/5

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3 cannot be a possible input for function C, 4  no function has a restriction on this input value and -4 → No function has a restriction on this input value.

What is function in mathematics?

In mathematics, a function is a rule that maps each element of a set (called the domain) to a unique element in another set (called the range or codomain).

A. The function rule is 3 divided by the input. The value that could not be a possible input for this function is 0 since division by zero is undefined.

B. The function rule is to add 4 to the input, then divide this value into 3. There is no value that could not be a possible input for this function.

C. The function rule is to subtract 3 from the input, then divide this value into 1. The value that could not be a possible input for this function is 3 since (3-3) = 0 and division by zero is undefined.

Therefore, the answers are:

1.3 → Cannot be a possible input for function C

2.4 → No function has a restriction on this input value

3.-4 → No function has a restriction on this input value

4.0 → Cannot be a possible input for function A

5.1 → No function has a restriction on this input value

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The correct answer is c. Line graphs show the change in one or more variables progressively across time.

Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.

The correct answer is c. Line graphs show the change in one or more variables progressively across time

A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.

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Line graphs show the change in one or more variables progressively across time. C

A line graph is a type of chart that displays data as a series of data points connected by straight lines.

The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.

By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.

Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.

They can be used to identify patterns, compare different variables, or forecast future trends.

In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.

Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.

Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.

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Answer:

Step-by-step explanation:

Use the law of cosines to find the side AB:

Use the Heron's area formula next:

Now

Next

Substitute this into the first equation:

Answer:

AB = 7 cm

Step-by-step explanation:

Sine Rule for Area

\(\sf Area =\dfrac{1}{2}ab \sin C\)

where:

Given:

Substitute the given values into the formula and solve for x:

\(\begin{aligned} \sf Area & = \dfrac{1}{2}ab \sin C \\\\\implies \sqrt{300} & = \dfrac{1}{2}(x+3)x \sin 60^{\circ}\\\\\sqrt{300} & = \dfrac{\sqrt{3}}{4}(x+3)x\\\\\dfrac{4\sqrt{300}}{\sqrt{3}} & = x^2+3x\\\\40 & = x^2+3x\\\\x^2+3x-40 & = 0\\\\ (x-5)(x+8)& = 0\\\\ \implies x & = 5, -8\end{aligned}\)

As length is positive, x = 5 only.

Substitute the found value of x into the expressions for the side lengths:

Cosine rule

\(c^2=a^2+b^2-2ab \cos C\)

(where a, b and c are the sides and C is the angle opposite side c)

Substitute the found values into the formula and solve for AB:

\(\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies AB^2 & =8^2+5^2-2(8)(5) \cos 60^{\circ}\\AB^2 & =89-40\\AB^2 & =49\\AB & =\sqrt{49}\\AB & = \pm 7\end{aligned}\)

As length is positive, AB = 7 cm.

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The answer is (a) (30, 50). To find the 98% confidence limits,

We can use the formula:

\(98% confidence limits = sample mean ± (Z-score for 98% confidence level) * (standard error)\)

We don't know the sample mean or the standard error, but we do know the 90% confidence limits. We can use these to estimate the standard error:

Standard error = (90% confidence limits upper bound - 90% confidence limits lower bound) / (1.645 * 2)

Standard error = (47 - 33) / (1.645 * 2) = 4.73

Now we can use this to estimate the 98% confidence limits:

98% confidence limits = sample mean ± (2.33) * (4.73)

We know that the range of the 90% confidence limits is 14 (47 - 33). The range of the 98% confidence limits will be wider than this, so we can eliminate options b), c), and e).

Now we just need to check which of the remaining options gives us a range wider than 14. We can do this by subtracting the lower limit from the upper limit:

a) (30, 50) -> range = 20
d) (38, 45) -> range = 7

Therefore, the answer is (a) (30, 50).

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If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.

In order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.

The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.

So, the probability of getting no defective products is:

P(none defective) = (1 - 0.075)³ = 0.6141

Therefore, the probability of getting at least one defective product is:

P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%

.So, the probability of getting at least one that is defective is 38.59%.

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Therefore, the derivative of h(z) is h'(z) = 4az/(a^2 - z^2)^2.

To differentiate the given function h(z) = ln[(a^2 - z^2)/(a^2 + z^2)], we use the chain rule and the quotient rule of differentiation.

The chain rule tells us that if we have a function inside another function, we must first differentiate the outer function with respect to the appropriate variable, and then multiply by the derivative of the inner function with respect to the same variable. In this case, we have the natural logarithm function inside the larger expression, so we use the chain rule to differentiate it.

The quotient rule tells us that if we have a fraction where the numerator and denominator are both functions of the same variable, we can differentiate the expression by first differentiating the numerator and denominator separately, and then combining them using a specific formula. In this case, we have a fraction where the numerator and denominator are both functions of z, so we use the quotient rule to differentiate it.

h'(z) = d/dz [ln[(a^2 - z^2)/(a^2 + z^2)]]

= 1/[(a^2 - z^2)/(a^2 + z^2)] * d/dz [(a^2 - z^2)/(a^2 + z^2)]

= (a^2 + z^2)/(a^2 - z^2) * d/dz [(a^2 - z^2)/(a^2 + z^2)]

= (a^2 + z^2)/(a^2 - z^2) * [(d/dz)(a^2 - z^2)/(a^2 + z^2) - (a^2 - z^2)/(a^2 + z^2)^2 * (d/dz)(a^2 + z^2)]

= (a^2 + z^2)/(a^2 - z^2) * [(2z)/(a^2 + z^2) - 2z/(a^2 - z^2)]

= 4az/(a^2 - z^2)^2

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Answer:

$28

Step-by-step explanation:

cp=20

mp=20%ofcp

=20/100*20

=8

now,

sp=mp+cp

=8+20

=28

Answer: B

Step-by-step explanation:

100/9

11.1

11 1/9

1 1/2 can be split apart into 1 as the whole part and 3/2 as the fractional part.

To split apart the mixed number 1 1/2 into its whole part and fractional part, we need to understand the components of a mixed number.

A mixed number consists of a whole number part and a fractional part. In this case, 1 1/2 is a mixed number where 1 is the whole number part and 1/2 is the fractional part.

To separate the whole part and fractional part, we can rewrite the mixed number as an improper fraction.

The whole number part, 1, can be written as a fraction with a denominator of 1:

1 = 1/1

Now, let's convert the fractional part, 1/2, into an improper fraction. To do this, we multiply the whole number part, 1, by the denominator of the fraction and add the numerator:

1 x 2 + 1 = 2 + 1 = 3

The improper fraction is 3/2.

So, we have the whole part as 1 and the fractional part as 3/2.

It's worth noting that the whole part represents the whole number portion of the mixed number, while the fractional part represents the remaining portion of the number that is less than a whole unit.

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The triangle ΔHIJ is an isosceles triangle, with congruent base angles ∠I and ∠H, and base HI. The legs of the isosceles triangle, IJ and JH are congruent, JH = 17, which indicates that IJ is 17

An isosceles triangle is a triangle that has two sides that have the same length.

The parameters in the question are;

∠I in ΔHIJ is congruent to ∠H

The length of segment JH = 17

The parameters in the question indicates that triangle ΔHIJ is an isosceles triangle.

The base angles of the triangle ΔHIJ are angle ∠I and angle ∠H

From the location of the base angles, the base of the isosceles triangle ΔHIJ is the side HI.

The legs of the isosceles triangle ΔHIJ are therefore. IJ and JH

IJ is congruent to JH by definition of isosceles triangles, therefore;

IJ ≅ JH

IJ = JH = 17

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4 3/4 pounds amount of sugar were left after Garth used 9 1/2 pounds for the lemonade.

9 1/2 pounds of sugar were used from 14 1/4 minus 4 3/4.

Garth needed 14 1/4 pounds of sugar to make lemonade for the school carnival, so he purchased them. He had 4 3/4 pounds of sugar left over when he had done preparing the lemonade. This indicates that he made the lemonade using 9 1/2 pounds of sugar. He took the 14 1/4 pounds of sugar he purchased and subtracted the 4 3/4 pounds that were leftover to get at the amount of sugar he utilised, or 9 1/2 pounds. This indicates that the correct response is D: The lemonade required 9 1/2 pounds of sugar.

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The volume of the can in terms of π is 90π cubic centimeters.

The surface area of an object refers to the overall space filled by its surfaces. Many 3D forms in geometry have various surface areas, which may be quickly estimated using the formulae we shall learn in this lesson. Two kinds of surface area exist: total surface area and lateral surface area, often known as curved surface area.

The can is in shape of a cylinder thus the volume of the cylinder is:

V = πr²h

Substitute the values:

V = π(3)²(10)

V = 90π

Hence, the volume of the can in terms of π is 90π cubic centimeters.

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Answer:

-2 1/2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-2 1/2

If a between-subjects design uses random assignment, the design will be called an independent groups design.

This means that participants are randomly assigned to either the experimental or control group, ensuring that the groups are equivalent at the start of the study. This type of design allows for a comparison of the effects of the independent variable on the dependent variable between the groups. I

t is important to note that an independent groups design is different from a matched groups design, in which participants are paired based on certain characteristics before being assigned to different groups. The use of random assignment in an independent groups design helps to control for extraneous variables and increase the internal validity of the study.

If a between-subjects design uses random assignment, the design will be called a(n) c. independent groups design. This design involves assigning participants to different experimental groups or conditions using random allocation. This ensures that each participant has an equal chance of being assigned to any group, reducing potential confounds and increasing the validity of the results. The independent groups design allows for comparison between the groups and the examination of the effects of the independent variable on the dependent variable.

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When the wheels of the new truck, with a radius of 18 inches, are rotating at 425 revolutions per minute, the truck will be moving at approximately  1.45 miles per hour

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius of the truck's wheels is 18 inches. To find the distance covered by the truck in one revolution of the wheels, we calculate the circumference:

C = 2π(18) = 36π inches

Since the wheels are rotating at 425 revolutions per minute, the distance covered by the truck in one minute is:

Distance covered per minute = 425 revolutions * 36π inches/revolution

To convert this distance to miles per hour, we need to consider the conversion factors:

1 mile = 5280 feet

1 hour = 60 minutes

First, we convert the distance from inches to miles:

Distance covered per minute = (425 * 36π inches) * (1 foot/12 inches) * (1 mile/5280 feet)

Next, we convert the time from minutes to hours:

Distance covered per hour = Distance covered per minute * (60 minutes/1 hour)

Evaluating the expression and rounding to the nearest whole number, we can get 1.45 miles per hour.

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The equation you mentioned, "15px," does not specify a conic section or provide enough information to determine the standard equation or describe the graph.

To determine the standard equation of a conic section with its center or vertex at the origin, you need more specific details about the conic section, such as its shape (circle, ellipse, parabola, or hyperbola) and additional parameters like the radius, semi-major axis, semi-minor axis, eccentricity, or focal length.
Once you have the necessary information, you can use the properties and characteristics of the specific conic section to derive its standard equation. The standard equations for different conic sections will have different forms and coefficients.
Please provide more information or clarify the conic section you are referring to so that I can assist you further in determining its standard equation and describing its graph.


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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The correct interpretation is that the total revenue generated at a production rate of 11 units is $368. The Correct option is:

d) None of the above.

The marginal revenue function R(x) represents the additional revenue generated by producing and selling one additional unit of a product. In this case, the marginal revenue function is given by R(x) = 500 - 12x.

The notation R(11) refers to evaluating the marginal revenue function at a production rate of 11 units, which means substituting x = 11 into the function. So, we have R(11) = 500 - 12(11) = 500 - 132 = 368.

The interpretation is that at a production rate of 11 units, the total revenue generated is $368.

This means that by producing and selling 11 units of the product, the company earns $368 in revenue.

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