Express each of the following trigonometric functions in terms of surds.a) cos (7/4 π)b) tan 240°

The logarithm of base 7 of t, as a logarithm of base 2 is given as follows:

log2(t)/log2(7).

A logarithm is defined as follows:

log_a(b).

In which:

To change the logarithm to a new base c, the logarithm is written by the fraction presented as follows:

log_c(b)/log_c(a).

In this problem, the logarithm is defined as follows:

log_7 t.

The new base is given as follows:

2.

(as stated in the problem, since we want the logarithm as a logarithm of base 2).

Hence, applying the change of base, the logarithm of base 2 will be given as follows:

log2(t)/log2(7).

As the term log2 represents the logarithm of base 2 of the term.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

10 tickets for $31.50

Step-by-step explanation:

So If we divide 22.75 by 7 it gives you 3 dollars and 25 cents per ticket

If you divide 31.50 by 10 it gives you 3 dollars and 15 cents.

So In conclusion 10 tickets for $31.50 dollars is the better buy

Answer:

10 Tickets Is The Better Deal

Step-by-step explanation:

So What You Do Is You Will Divide 22.75 By 7

You Will Get 3.25! That Means Its 3.25 Each For 7 Tickets

For The Next One You Do The Same Thing

You Want To Divide 31.50 By 10

You Will Get 3.15! That Means Its 3.15 Each For 10 Tickets

So 3.15 Is 10 Cheaper Than 3.25 So Getting 10 Tickets Is A Better Deal

Hope This Help

DOH! My Brain Hurts

Answer:

Step-by-step explanation:

Essentially, recall what an absolute value function is.

When you plug number into an absolute value function, or make it an absolute value, you will ALWAYS get a positive version of that number.

When the question asks, what number could be the absolute value of another number, it's asking you what is a possible outcome of making a number an absolute value.

Since we know that making any number an absolute value, makes that number positive. We can get rid of all of the negative answers.

You are left with B.

Answer:

B. 1200

Step-by-step explanation:

Absolute value is the non-negative version of a number/variable. Whether the sign is negative or positive, the absolute value is always positive.

Example:

|-4|=4
|2|=2

Answer:

Step-by-step explanation:

1st 10 days - 8 GB

2nd 10 days - 8 GB

3rd 10 days - 8 GB

________________

30 days    -  24 GB

Its the last one. I just took the quiz on edge.

Step-by-step explanation: The scale factor is 5. You mutiply  5 with the coordinates. J  is (-3,2) so multiply 5 and -3  which is -15 then do the same thing with 2 which equals 10. J'=(-15,10)

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Answer: Number 1 Is also ∠ABC and it is a right triangle

Number 2 is CB and BE

Number 3 is 18

Step-by-step explanation:

Step-by-step explanation:

1.

angle ABD

2.

CB and BE

3.

"bisects" means it is cutting it in half.

so, angles 3 and 4 are both half of the main angle 94°.

94/2 = 47°

angle CBE = angle 4 = 47° = (3x - 7)°

3x - 7 = 47

3x = 54

x = 18

It takes them 12 hours to design a total of 7 logos if they both start working at the same time

This is the amount per unit time.

Since one graphic designer takes 3 hours to design a logo. Her less experienced colleague takes 4 hours to design a logo, we need to find the rate at which the work is done.

Now, since we require the time to desigh 7 logos, this time is T = number of logos/combined rate

= 7 logos ÷ 7/12 logo/hr

= 12 hr

So, it takes them 12 hours to design a total of 7 logos if they both start working at the same time

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The additional 60 men, the provisions will last for approximately 20 weeks.

To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.

Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.

Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.

To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:

Provisions last = Total person-weeks / Number of men

= 9200 / 460

≈ 20 weeks (rounded to the nearest whole number)

The additional 60 men will extend the supply's shelf life to around 20 weeks.

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Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

The 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7 is \(\frac{7}{19683}\).

What is  geometric sequence?

A unique kind of sequence is a geometric sequence. Every term in the series (apart from the first term) is multiplied by a fixed amount to determine the following term. In other words, we multiply the current phrase in the geometric sequence by a constant term (called the common ratio), and then divide the current term in the geometric sequence by the same common ratio to discover the previous term in the geometric sequence.

nth term of geometric series

a(n) = a(1) * r^(n-1)

You are given a(1) = 7, r = 1/3 and n = 10.

a(10) = 7 * 1/3^(10-1)

\(7\left(\frac{1}{3}\right)^{10-1}$$\)

Apply exponent rule: \($\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$\)

\($$\begin{aligned}& \left(\frac{1}{3}\right)^{10-1}=\frac{1^{10-1}}{3^{10-1}} \\& =7 \times \frac{1^{10-1}}{3^{10-1}}\end{aligned}$$\)

\($$\begin{aligned}& 1^{10-1}=1 \\& =7 \times \frac{1}{3^{10-1}} \\& 3^{10-1}=19683 \\& =7 \times \frac{1}{19683}\end{aligned}$$\)

Convert element to fraction: \($\quad 7=\frac{7}{1}$\)

\(=\frac{7}{1} \times \frac{1}{19683}$$\)

Apply the fraction rule: \($\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$\)

\(=\frac{7 \times 1}{1 \times 19683}$$\)

Multiply the numbers: \($7 \times 1=7$\)

\(=\frac{7}{1 \times 19683}$$\)

Multiply the numbers: \($1 \times 19683=19683$\)

\(=\frac{7}{19683}\)

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The type of experimental design where the assignment of Experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).

The type of experimental design where the assignment of experimental units to treatment and control groups is random is called a randomized controlled trial (RCT).

Randomized controlled trials are widely used in various fields of research, including medicine, psychology, and social sciences. They are considered the gold standard for evaluating the effectiveness of interventions or treatments. The key feature of an RCT is the random assignment of participants or experimental units to either the treatment group or the control group.

Randomization helps to ensure that the treatment and control groups are similar in terms of both observed and unobserved characteristics, reducing the potential for bias and confounding variables. By randomly assigning participants, researchers can make causal inferences about the effects of the treatment, as any observed differences between the groups can be attributed to the intervention.

In an RCT, experimental units can be individuals, groups, organizations, or any other defined units depending on the research context. The random assignment process involves using a randomization procedure, such as coin flipping, random number tables, or computer-generated randomization, to assign participants to the treatment and control groups.

By comparing the outcomes or responses of the treatment and control groups, researchers can determine the effectiveness or impact of the intervention being studied. Statistical techniques, such as hypothesis testing and analysis of variance, are commonly used to analyze the data collected from the RCT and draw conclusions.

a randomized controlled trial is the type of experimental design where the assignment of experimental units to treatment and control groups is random. It is a rigorous approach to evaluating the effects of interventions and minimizing biases, providing robust evidence for decision-making and policy development.

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Multiply 15 and 6.8. So speed * time = distance

So the answer is 102

Answer:

im sorry i dont know i like ur pfp tho!! :3

Step-by-step explanation:

i dont know i like ur pfp tho!! :3

The slope (m) of the MB is: 1. The equation of the line of MB is: y = x.

We can express the equation of a line in slope-intercept form as, y = mx + b, where we have:

Slope = m = change in y / change in x

y-intercept = b.

Given the points, M(-4,-4) and B(-1,-1), to find the equation that the points lie on, first, find the slope of MB:

Slope (m) = (-4 -(-1))/(-4 -(-1))

Slope (m) = -3/-3

Slope (m) = 1

Substitute (x, y) = (-1, -1) and m = 1 into y = mx + b to find b

-1 = 1(-1) + b

-1 = -1 + b

-1 + 1 = b

b = 0

Substitute m = 1 and b = 0 into y = mx + b

y = 1(x) + 0

y = x.

Thus, the slope (m) of the MB is: 1. The equation of the line of MB is: y = x.

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The family’s fuel efficiency in miles per gallon is 32.67miles/gallon .The cost of their 1060-mile route if gasoline costs $2.35 per gallon  is $ 76.234.

The measure of the length between two points is called Distance.

It is a scalar quantity.

The family's fuel efficiency =  Distance travelled/ Fuel required

= 750/54

= 13.89 km/l

= 13.89* 0.621/0.264  miles/gallon

=32.67miles/gallon

For the same fuel efficiency ,

cost for Washington DC trip

Distance = 1060 mile

fuel required = 1060/32.67

=32.44 gallon

Cost of 1 gallon = $2.35

Cost of 32.44 gallon = 32.44 * 2.35

=$76.234

The cost of their 1060-mile route if gasoline costs $2.35 per gallon  is $ 76.234.

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Answer:

81.12 cm²

Step-by-step explanation:

The area for a semicircle can be figured with this formula: (πr²)/2. The triangle's area formula is bh/2.

(3.14 * 4²)/2 + (14 * 8)/2 (Work the operations in parentheses first.)

(3.14 * 16)/2 + 112/2

50.24/2 + 112/2 (Divide 50.24 by 2. Do the same for 112.)

25.12 + 56 (Add 25.12 & 56.)

81.12 cm²

The area of the figure is 81.12 cm².

i saw the answer should be 20 character so the answer is

Loki

superman

batman

Ironman

Spiderman

Hulk

thor

Black widow

vision

scarlet witch

flash

green lantern

Thanos

star lord

wonder woman

super girl

cat women

hella

grandmaster

cyborg

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

sin = -√2 / 2

cos = √2 / 2

tan = -1

Step-by-step explanation:

Θ is in quad IV

sin = -√2 / 2

cos = √2 / 2

tan = -1

Answer:

Step-by-step explanation:

1. A + B

2. 9 + u - 10

3. m - 2 / 2

Answer:

2.4*18 = $43.2

stock price is $43.2

Step-by-step explanation:

There are 125 stickers did Sally have to start.

We have to given that,

Sally had 52 more stickers than Joe after Joe gave 1/5 of his stickers to her.

Let us assume that,

Joe had x stickers to start with.

Since, After Joe gave 1/5 of his stickers to her.

He have 4/5 of his original amount left.

That is, 4/5x

Since, Sally had 52 more stickers than Joe

Hence, We get;

4/5x + 52 = 1/5x + y  .. (i)

where y is the number of stickers Sally had to start with.

Here, they both had a total of 260 stickers,

Hence,

x + y =260  .. (ii)

From (i) and (ii);

y = 125

Thus, There are 125 stickers did Sally have to start.

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Answer:

5x 2

Step-by-step explanation:

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

Using proportions, the adjusted lifetime risk of stroke if every member of the population adds 25 grams of white fruits and vegetables to their daily diet is of 7.34%.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships.

One example of application of proportions is for percentage problems, as the decimal equivalent of the percentage is multiplied to the total amount to find the equivalent amount.

807 persons out of 10,000 persons in a particular population suffer a stroke sometime in their lifetime, hence the risk is given by:

r = 807/10000 = 0.0807.

A 9% decrease means that the adjusted risk will be of 91% of that amount, hence:

0.91 x 0.0807 = 0.0734 = 7.34%.

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Answer: 69.8°F

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

24 feet ÷3/5 =

24/1 × 5/3 =

40