If x = logb2 and y = log b5, express log b100 in terms of x and y.

logb100=____?​

Answer:

cosΘ = [tex]\frac{\sqrt{21} }{5}[/tex]

Step-by-step explanation:

using the identity

• sin²Θ + cos²Θ = 1 ⇒ cos²Θ = 1 - sin²Θ

given Θ is in quadrant 1 , then cosΘ > 0

sinΘ = [tex]\frac{2}{5}[/tex] , then

cos²Θ = 1 - ( [tex]\frac{2}{5}[/tex] )² = 1 - [tex]\frac{4}{25}[/tex] = [tex]\frac{25}{25}[/tex] - [tex]\frac{4}{25}[/tex] = [tex]\frac{21}{25}[/tex] , then

cosΘ = [tex]\sqrt{\frac{21}{25} }[/tex] = [tex]\frac{\sqrt{21} }{\sqrt{25} }[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]

The mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

A physical combination of two or more unrelated substances is referred to as a mixture. For instance, water and salt are two different substances that, when combined, form a combination.

Let's call the amount of cashews used in pounds "x". The amount of Brazil nuts used in pounds can be calculated as 30 - x.

We know that the total cost of the mixture is $6.08 per pound * 30 pounds = $182.40.

The cost of the cashews in the mixture is $7.70 per pound * x pounds =$7.70x.

The cost of the Brazil nuts in the mixture is $5.00 per pound * (30 - x) pounds = $150 - $5.00x.

The total cost of the cashews and Brazil nuts in the mixture must equal $182.40, so we can set up the equation:

$7.70x + ($150 - $5.00x) = $182.40

Expanding and simplifying the equation:

$2.70x = $32.40

Dividing both sides by 2.70:

$x = 12

So, the mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

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The first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

What is the first quartile of the data set?

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

Since we have given a box and whisker plot.

As we know about the box and whisker method that :

Left most part of the box represents the first quartile and the rightmost part of the box represents the third quartile.

And the middle value is for median

so, we can conclude that

First quartile = 20

Third quartile = 40

Median = 25

Hence, the first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.

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On solving the provided question, we can say that  x = central angle = 60 degrees, r = radius = 9 inches and L = 9.42

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

x = central angle = 60 degrees

r = radius = 9 inches

L = arc length

[tex]L = (x/360)*2*pi*r\\L = (60/360)*2*pi*9\\L = 3*pi\\L = 9.42477796076938\\L = 9.42[/tex]

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Using the equation provided, you can estimate the number of hours worked each week for a student with a GPA of 2.21. The equation can be rearranged to solve for h, the number of hours worked each week.

h = (g - 3.04) / (0.012 + 0.0007)

Plugging in the GPA of 2.21, we get:

h = (2.21 - 3.04) / (0.012 + 0.0007)

h = -4.83 hours

Therefore, a student with a GPA of 2.21 would need to work an average of -4.83 hours per week in order to achieve that GPA.

Answer:

120°

Step-by-step explanation:

We need to find the missing angle <SRM

The angles inside a triangle always add up to 180°. So this means:

<TSR+<STR+<TRS=180°

65°+55°+<TRS=180°

120°+<TRS=180°

<TRS=180°-120°=60°

All angles along a straight line add up to 180°. This means:

<TRS+<SRM=180°

60°+<SRM=180°

<SRM=180°-60°=120°

Answer:

120° is the answer please mark. brainly

Answer: a) 1.57 m .

b) 637.79 turns

Step-by-step explanation:

a) The circumference of the wheel can be used to determine how far the vehicle has travelled after making one full turn.

Circumference = 2πr = 50π

C = 157 cm

b)By dividing the entire distance traveled by the diameter of the wheel, we can determine how many times the wheel will turn over a ride of 1 km (1000 meters): 1000 m / 1.57 m = 637.79 turns.

Answer:

a

Step-by-step explanation:

"Communist infiltration in the entertainment industry" was the first target of the HUAC hearings among the following choices given in the question.

HUAC was created in 1938 to investigate alleged disloyalty and rebel activities on the part of private citizens, public employees and organizations suspected of having Communist ties.

Originally organized as a minor congressional committee investigating domestic subversion, HUAC (also known as the House Un-American Activities Committee) rose to such power in the late 1940's and early 1950's that the mere threat of investigation by it could ruin a person's career. By the time it was abolished in 1975, HUAC had widened its scope of investigation to include almost every aspect of American society.

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Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

Average = (Sum of all values) / (Number of values)

Average = ($19) / (7 days)

Average = ($19) / (7)

Average = $2.71

Sunday = ($2.71) x (7)

Sunday = $19.00 + $76.00

Sunday = $95.00

Jack is working as a waiter and needs to keep track of his tips. He wants to make an average of $19 per day and needs to figure out how much he needs to make on Sunday. To calculate this, he needs to first figure out the average he wants to make per day. For this, he needs to divide the amount he wants to make daily ($19) by the number of days he is working (7). This gives him an average of $2.71 per day. To get to the amount he needs to make on Sunday, he needs to multiply this average by the number of days he is working, which is 7. This gives him an amount of $19.00 + $76.00, which equals $95.00. Thus, Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.

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Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

60% i mean it sounds right

Step-by-step explanation:

We can know that she can be any value but these 15 times the value of C. The given system is consistent to all the possible values of f and g, the reduction of the row of the augmented matrix must not result in the row of form  [0 0 ... 0 | b]where  B is nonzero.

By looking the row reduction in the system we can see the 2nd row reduces to  [0 0 ...0 | d-15c-g+f]. Since f and g can be any values we can make them both 20 which denotes d - 15 C is equals to zero, or d equals to 15C.

d-15c = 0, or d = 15c.

Therefore we can know that she can be any value but these 15 times the value of C.

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Answer:

30 mm

Step-by-step explanation:

just add the length of each side together

Answer: To find the total weight of 400 apples, we need to multiply the number of apples by their weight. Each apple weighs 1/4 pound, so 400 apples weigh 400 * (1/4) = 100 pounds.

Since each bag should weigh 5 pounds, we can divide the total weight of apples (100 pounds) by 5 to find the number of bags: 100 / 5 = 20 bags.

So, the answer is 20 bags.

Step-by-step explanation:

On solving the provided question we can say that median from the vertex in an isosceles triangle is perpendicular to the base.

ƒ(x)=sin(x)

consider Asin(Bx + C) = y +D changes the amplitude of the function (how high or low it is).

if you want to

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Let O be the circle's centre and P be the midpoint of BC. After that, OP LBC.

Let AP =x and PB = CP -y.

Applying Pythagoras theorem in As AP B and OP B, we have

AB2 = BP2 + AP2 and OB2 = OP2 +BP2

Y2 +x2 ... (i) and, 81 = (9 —x)2 + Y2

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The expression  x²−−6 can be factored as:

[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]

What is Factoring an expression?

A numerical or algebraic expression is factored when it is written as a product of factors. The distributive property can be used to factor expressions.

The expression  x²−−6 can be factored as:

[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]

The solutions for this equation would be x = √6 or x = -√6. These are the values of x that make the expression equal to zero.

Factoring the expression in this way can be useful in solving related equations or in finding the roots of a quadratic function. It also helps in visualizing the graph of the function, as the factored form shows the x-intercepts, which are the points where the graph crosses the x-axis.

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Answer:

[tex] \sf \: f(2) = - 2[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 4x - 5x

Now we have to,

→ Find the required value of f(2).

Then the value of f(2) will be,

→ f(x) = 4x - 5x

→ f(2) = 4(2) - 5(2)

→ f(2) = 8 - 10

→ [ f(2) = -2 ]

Hence, the value of f(2) is -2.

Answer: A) 6

Step-by-step explanation:

This is geometry. The two angles are corresponding angles, because they are both cut by the same **transversal line**. When that occurs, corresponding angles are created.

now importantly: corresponding angles are equal to each other, or **congruent**. Knowing this, we can set them equal to each other.

17x+11=19x-1

Solve...

11=2x-1

12=2x

x=6

hope this helps

MM

Using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Once we have determined the value of a single unit, we may multiply that value by the number of units needed to determine the value of the other units. The concept of ratio and proportion is mostly applied using this way. Recognizing the units and values is crucial when using the unitary technique to a problem.

Given,

    Money received for each document = 25 cents

  Number of documents prepared by Bill = 2000

  The amount he received = $474

a) The correct total pay that Bill should receive = 2000*25 = 50,000cents

   Using the unitary method,

                   1 dollar = 100 cents

                  50,000 cents = 50000/100 = $500

b) The amount that his boss owes him = 500 - 474 = $26

Therefore using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.

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The Possible effects of incentives for political leaders includes options 1, 2, 3, and 4. These options elaborate the incentives of political leaders.

Favor programs with immediate benefits: Political leaders may be incentivized to prioritize policies or programs that provide immediate benefits to their constituents in order to increase their popularity and chances of reelection.

Implement policies that favor a small, powerful group: Incentives for political leaders may also lead them to implement policies or regulations that favor a small, powerful group, such as major donors or influential interest groups, at the expense of the general public.

Provide policies whose costs outweigh the benefits: Political leaders may be incentivized to implement policies that provide short-term benefits but have long-term costs or consequences, such as a large budget deficit or environmental degradation.

Favor programs with immediate costs: Alternatively, incentives may lead political leaders to prioritize programs or policies with immediate costs, such as increased taxes or reduced spending, to address pressing issues and avoid long-term consequences.

Therefore, options 1, 2, 3, and 4 describe possible effects of incentives for political leaders.

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____The given question is incomplete, the complete question is given below:

Select all the items that describe possible effects of incentives for political leaders. 1.favor programs with immediate benefits 2.implement policies that favor a small, powerful group 3.provide policies whose costs outweigh the benefits 4.favor programs with immediate costs

On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic

volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic

total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.

Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic

Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18

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Answer:

  45°

Step-by-step explanation:

Given a polygon with an interior angle of 135°, you want to know the measure of the corresponding exterior angle.

At any given vertex of a polygon, the interior and exterior angles are supplementary:

  exterior angle = 180° - interior angle

  exterior angle = 180° -135°

  exterior angle = 45°

Answer: The sum of the interior angles of a regular polygon can be found using the formula:

(n-2)180°, where n is the number of sides of the polygon.

Let's call the number of sides of the polygon "s".

We know that one of the interior angles is 135°, so we can set up an equation using the formula for the sum of the interior angles:

s * 135° = (s-2)180°

Expanding the right side of the equation:

s * 135° = (s-2) * 180°

s * 135° = s * 180° - 360°

Solving for s:

135° = 180° - 360°/s

135° = 180° - 2 * 180°/s

135° = 180° - 2 * (180°/s)

180° - 135° = 2 * (180°/s)

45° = (180°/s)

So, s = 180° / 45° = 4 sides.

The size of one exterior angle can be found by subtracting each interior angle from 360°:

360° - 135° = 225°.

Therefore, one exterior angle of the polygon is 225°.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).

The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).

The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:

1/36 * 1/36 = 1/1296

So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let the time taken by Jeeny in both the cases be " t " ~

Now, during upstream : current flow opposes the flow of swimmer (Jenny)

Let her actual speed without current be " v ", so her speed in current (upstream) will be :

[tex]\qquad \sf  \dashrightarrow \: v - 1 \: \: kmph[/tex]

Now, according to formula :

[tex]\qquad \sf  \dashrightarrow \: distance = speed \times time[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8 = (v - 1)t \: \: \: \: \: - (1)[/tex]

Next, durijg dowstream : current flow supporta the flow of swimmer (Jenny)

So, her speed while going downstream will be :

[tex]\qquad \sf  \dashrightarrow \: v +1 \: \: kmph[/tex]

By same formula,

[tex]\qquad \sf  \dashrightarrow \: 16 = (v + 1)t \: \: \: \: \: - (2)[/tex]

Now, solve the two equations ~

[ since time taken by her in both the cases is same, we use t in both equations ]

Divide equation (1) by equation (2) :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{8}{16} = \dfrac{v - 1}{v + 1} [/tex]

[ t gets canceled out ]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{2} = \dfrac{v - 1}{v + 1} [/tex]

[ cross multiply ]

[tex]\qquad \sf  \dashrightarrow \: v + 1 = 2(v - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v + 1 = 2v - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2v - v = 1 - ( - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 1 + 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 3 \: \: kmph[/tex]

That's the required answer ~ [ Jimmy would swim at the rate of 3 kmph if she there was no current ]

Answer:

Step-by-step explanation:

here is a step-by-step explanation for finding the equation of the line that passes through the points (0, -3) and (0, -8):

Identify the two points that the line passes through: (0, -3) and (0, -8)

Determine the slope of the line: The slope of a line is given by the formula "rise over run," or (y2 - y1) / (x2 - x1). However, in this case, the line is vertical and has an undefined slope.

Write the equation of the line in slope-intercept form: y = mx + b, where "m" is the slope and "b" is the y-intercept. Since the slope of the line is undefined, the equation of the line cannot be written in slope-intercept form.

Write the equation of the line in point-slope form: y - y1 = m(x - x1), where "m" is the slope and (x1, y1) is a point on the line. Since the slope of the line is undefined, the equation of the line cannot be written in point-slope form.

Write the equation of the line as an x-intercept form: The x-intercept form of a line is given by the equation x = a, where "a" is the x-coordinate of the point that the line passes through. In this case, the line passes through the point (0, -3) and (0, -8), so the equation of the line is x = 0.

So, the equation of the line that passes through the points (0, -3) and (0, -8) is x = 0.

In linear equation, $ 618,418.80  will Andrea and Stanley save by choosing Mortgage A .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Total Payback = Instalment Amount * No. of Instalments

Mortgage A:

=  $1621.39 * 360

= $ 583,700.40

Mortgage B:

=  $1717.83 * 360

=$ 618,418.80

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Answer: The simple interest on 16000 at 5% per annum for 1.5 years is calculated as:

I = P * r * t

I = 16000 * 0.05 * 1.5

I = 1200

The compound interest on 16000 at 5% per annum compounded half yearly for 1.5 years is calculated as:

A = P * (1 + r/n)^(nt)

A = 16000 * (1 + 0.05/2)^(2 * 1.5)

A = 16000 * (1.0253)^3

A = 16000 * 1.07897

A = 17253.576

The difference between the compound interest and simple interest is:

17253.576 - 1200 = 16053.576

So the difference between the simple interest and compound interest is 16053.576.

Step-by-step explanation:

The future value of the investment when interest is compounded continuously is; $3408.29

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

P= $1500, r = 3.95%, t = 5 yr

To Calculate the number of periods: in this case we have 5*12= 60 months.

- The monthly interest rate, we have to divide the annual nominal rate by 12 (the number of periods in the year).

Then, we can calculate the future value as:

A = P (1 + r/n)^nt

A = 1500(1 + 3.95/365)(365)^(5)

P = 1500/ (1 + 0.00010137)^(5)

P = $3408.29

The future value when compounded monthly is $3408.29.

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Answer Option C

The point-slope form of the equation of the line is:

Where m is the slope and b is the intersection with the y-axis.

In the line , you can identify that:

The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).

Then the answer is the option C.

please mark me brainliest

Answer:

C

Step-by-step explanation:

Area A should be the shaded region instead of the region shaded on the graph.