Rewrite the expression as a single logarithm

Please help will give brainlist only if correct!

In the given origami of the two dimensional figure , the value of angle 2 is 70° and the value of angle 1 is 110 °

Parallel lines are straight lines that do not intersect at any point in geometry.

Parallel planes are three-dimensional pathways that never intersect. Parallel curves do not touch or intersect and have a fixed minimum distance.

From the figure we can see that m∠1 = 4x-30 as they are vertically opposite angles.

Again m∠1 = 3x+5 as they are corresponding angles from the pair of parallel lines.

now let us solve the linear equation to calculate the value of x.

3x+5 = 4x-30

or, -x = -35

or, x = 35

Now

m∠1 = 3x+5 = 110

Therefore m∠2 = 180 -110 = 70 ( straight angle formed whose sum is 180)

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Answer:

0.02

Step-by-step explanation:

Given a normal distribution :

Mean income (m) = 25000

Standard deviation of income (s) = 6000

X ≥ 12000

Using the relation to fund the standardized score :

Zscore =(x - m) / s

Zscore = ( 12000 - 25000) / 6000

Zscore = -13000 / 6000

Zscore = - 2.167

Using a z probability calculator :

P(Z ≤ - 2.167) = 0.015117

= 0.02

Answer:

18 cars

Step-by-step explanation:

6 times 2= 12 boats

3 times 6= 18 cars

Hopefully this helps!

Answer:

He has 36 cars if there are 12 boats

Step-by-step explanation:

If he has 3 cars for every 2 boats he has then he would have 36 cars. You multiply 12 and 3 to get 36.

Answer:

$0.85

Step-by-step explanation:

if you multiply 7x0.76=5.32

and then subtract the 6.17-5.32=$.85

Answer:

.85

Step-by-step explanation:

Multiply .76x7 then subtract 5.32 from 6.17 and you get 0.85.

Answer:

The first quartile of the strengths of this alloy is 9.055 GPa.

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The strength of an aluminum alloy is normally distributed with mean 10 gigapascals (GPa) and standard deviation 1.4 GPa.

This means that \(\mu = 10, \sigma = 1.4\)

What is the first [lower] quartile of the strengths of this alloy?

This is the 100/4 = 25th percentile, which is X when Z has a pvalue of 0.25, so X when Z = -0.675.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.675 = \frac{X - 10}{1.4}\)

\(X - 10 = -0.675*1.4\)

\(X = 9.055\)

The first quartile of the strengths of this alloy is 9.055 GPa.

Answer:

I can't see the problem, sorry.

Answer:

Option D

Step-by-step explanation:

Measure of adjacent side = 20

Measure of Hypotenuse = 24

Since, measures of adjacent side and Hypotenuse have been given in the question, cosine ratio will be applied to find the measure of angle x.

cos(x) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

cos(x) = \(\frac{20}{24}\)

x = \(\text{cos}^{-1}(0.833)\)

  = 33.55°

  ≈ 33.6°

Option D is the answer.

Answer:

Two examples of points that satisfy this condition is (0,5) and (0,-5).

Step-by-step explanation:

Suppose we have two points:

\(A = (x_{1}, y_{1})\)

\(B = (x_{2}, y_{2})\)

The distance between these points is:

\(D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

In this question:

B(0,0)

A(x,y)

We have to find x and y.

We have that:

\(\sqrt{(x-0)^{2} + (y-0)^{2}} = 5\)

\(\sqrt{x^{2} + y^{2}} = 5\)

\((\sqrt{x^{2} + y^{2}})^{2} = 25\)

\(x^{2} + y^{2} = 25\)

One example of a point:

I will say that x = 0. So

\(0^{2} + y^{2} = 25\)

\(y = \pm \sqrt{25}\)

\(y = \pm 5\)

So two examples of points that satisfy this condition is (0,5) and (0,-5).

The distance formula is a formula that is used to find the distance between two points.

The coordinate of point A is (0, 5)  or   (0, -5).

Let us consider that, coordinate of point A is (x, y).

The distance between (0,0) and (x, y) is computed as by using distance formula.

                 \(Distance=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\5=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\x^{2} +y^{2}=25\)

All values that satisfies above equation, will be the coordinate of point A.

When x = 0,  

                \(y=\sqrt{25} =\pm 5\)

The coordinate of point A is (0, 5)  or   (0, -5).

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Answer:

Step-by-step explanation:

A) Let x represent minutes used, and C represent monthly charge. We are given two (x, C) pairs: (370, 133.00) and (530, 181.00)

We can use these in the 2-point form of the equation for a line.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  C = (181 -133)/(530 -370)(x -370) +133

  C = 48/160(x -370) +133

  C = 0.30x -111 +133

  C = 0.30x +22

__

B) For x = 477 minutes, the charge will be ...

  C = 0.30(477) +22 = $165.10 . . . . for 477 minutes

The monthly cost C =   $22 + $0.30x

Jane's bill for August is $165.10

The total amount Jane pays is the sum of the monthly fee and the charge per minute.

Total amount = monthly fee + charge per minute

Two equations can be derived from the question

a + 370b = 133 equation 1

a + 530b = 181 equation 2

Where:

a = monthly fee

b = charge per minute

This equation would be solved using simultaneous equation

Subtract equation 1 from equation 2

160b = 48

Divide both sides of the equation by 160

b = 48 / 160

b = 0.30

Substitute for b in equation 1

a + 370(0.30) = 133

a + 111 = 133

a = 133 - 111

a = 22

Based on the above calculations,  the monthly fee is $22 and the charge per minute is $0.30

Equation for monthly cost = $22 + $0.30x

If Jane used 477 minutes, total charge :

$22 + $0.30(477) =

22 + 143.10

= $165.10

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Answer:

The volume of the bookshelf is 180000 cm³.

Step-by-step explanation:

The dimensions of the bookshelf are 40 cm, 50 cm and 900 mm.

We know that,

1 mm = 0.1 cm

900 mm = 90 cm

Now the dimensions become 40 cm, 50 cm and 90 cm.

The volume of the bookshelf can be calculated as :

V = lbh

Substitute all the values,

V = 40 cm × 50 cm × 90 cm

V = 180000 cm³

So, the volume of the bookshelf is 180000 cm³.

Answer:

Option (2)

Step-by-step explanation:

Given:

∠1 ≅ ∠3

To Prove:

∠AXD ≅ ∠CXB

Solution:

Given question is incomplete; find the complete question in the attachment.

            Statements                                                              Reasons

1). m∠1 ≅ m∠3 because m∠1 ≅ m∠3          1). Given

2). m∠1 + m∠2 = m∠CXB and                    

    m∠2 + m∠3 = m∠AXD                            2). Angle addition postulate

3). m∠1 + m∠2 = m∠AXD                             3). Because you can substitute

                                                                          m∠1 for m∠3

4). m∠CXB = m∠AXD                                   4).Transitive property of equality

5). ∠AXD ≅ ∠CXB

Therefore, Option (2) will be the correct option.

The null and alternative hypotheses can be stated as follows:

c. H0: µ = 12, Ha: µ ≠ 12

The null hypothesis (H0) assumes that the population mean content of the bottles is 12 ounces, indicating perfect adjustment of the filling machine. The alternative hypothesis (Ha) states that the population mean content is not equal to 12 ounces, suggesting that the machine is not in perfect adjustment.

The rejection region for α = 0.01 can be specified as:

c. |t| > 2.68

This means that we would reject the null hypothesis if the absolute value of the calculated t-statistic is greater than 2.68.

To calculate the p-value, we need the t-statistic corresponding to the sample mean and standard deviation. With a sample mean of 11.88 ounces, a standard deviation of 0.35 ounces, and a sample size of 49, we can calculate the t-statistic. The p-value represents the probability of observing a sample mean as extreme as the one obtained, assuming the null hypothesis is true.

The p-value cannot be determined without the t-statistic value or the corresponding degrees of freedom.

Without the p-value, we cannot draw a definitive conclusion. To make a conclusion, we would compare the calculated t-statistic to the critical t-value based on the chosen significance level (α = 0.01). If the calculated t-statistic falls within the rejection region (|t| > 2.68), we would reject the null hypothesis. If the calculated t-statistic falls outside the rejection region, we would fail to reject the null hypothesis.

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The number of  mac and cheese Abdullah can buy for $20 is 8.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, at the grocery store, Abdullah purchased 3 pounds of mac and cheese for $7.50.

Now, cost of 1 pound of mac and cheese =Total cost/Number of pounds of mac and cheese

= 7.50/3

= $2.50

Then, with $20 Abdullah can by =20/2.50

= 8

Therefore, the number of  mac and cheese Abdullah can buy for $20 is 8.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

1 answer

Answer:lower bound = 147.5gupper bound = 152.5gStep-by-step explanation:if you were rounding a single digit number to the nearest 5, ...

Step-by-step explanation:

From the diagram given, we can see that line a is parallel to line b. This means that the position of each of the angle on line a is equal to the position of each of the angle in line b

From the figure <1 = <(7x+19)degree (corresponding angle). Also <5 = 7x+19 = <1 (corresponding angle as well)

From the above, we can say that <5 = <1 and since <5 and <6 lies on the same stright line, their sum will be 180.

Don't forget that <5 is now replaced as <1. Hence <1+<6 = 180 (supplementary angle).

From the expalnation above, the theorems that was used to prove the relationship between <1 and <6 are supplementary angle, corresponding angle and same side interior angle

Hence option D is correcct

\(\\ \sf\longmapsto 3x-4y=-12\)

\(\\ \sf\longmapsto 3x+12=4y\)

\(\\ \sf\longmapsto y=\dfrac{3x+12}{4}\)

\(\\ \sf\longmapsto y=\dfrac{3}{4}x+\dfrac{12}{4)\)

\(\\ \sf\longmapsto y=\dfrac{3}{4}+3\)

Answer:

Step-by-step explanation:

According to the central limit theorem, if independent random samples of size n are repeatedly taken from any population and n is large, the distribution of the sample means will approach a normal distribution. The size of n should be greater than or equal to 30. Given n = 100 for both scenarios, we would apply the formula,

z = (x - µ)/(σ/√n)

a) x is a random variable representing the salaries of accounting graduates. We want to determine P( x > 52000)

From the information given

µ = 50402

σ = 6000

z = (52000 - 50402)/(6000/√100) = 2.66

Looking at the normal distribution table, the probability corresponding to the z score is 0.9961

b) x is a random variable representing the salaries of finance graduates. We want to determine P(x > 52000)

From the information given

µ = 49703

σ = 10000

z = (52000 - 49703)/(10000/√100) = 2.3

Looking at the normal distribution table, the probability corresponding to the z score is 0.9893

c) The probabilities of either jobs paying that amount is high and very close.

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

Answer:

y-intercept: (0,7)

x-intercept: (3.5,0)

Step-by-step explanation:

The equation is in slope-intercept form.

\(y = mx + b\\\rule{150}{0.5}\\m - \text{slope}\\b - \text{y-intercept}\)

Since '7' is in b's spot, it is the y-intercept of the equation.

(0,7)

To find the x-intercept, we would plug 'y' in for 0 and solve for x.

\(y = -2x + 7\\\rule{150}{0.5}\\0 = -2x + 7\\\\0 - 7 = -2x + 7 - 7\\\\-7 = -2x\\\\\frac{-7=-2x}{-2}\\\\\boxed{x = 3.5}\)

The x-intercept is (3.5, 0).

Hope this helps.

Answer:

the markup is 1.26 (the amount added is .26)

1.26x (when x is the price Fred buys them for from the manufacturer)

1.26(40)

$50.40 is the retail price

50.4-40

$10.40 is the markup

Step-by-step explanation:

The 26% markup means that he is selling the flags 26% above the cost.

So, the cost would represent 100%, which is 1, and 26% of markup in decimal number is 0.26.

The price including the markup would be 1.26 as decimal or 126% as percentage.

The problem states that the cost is unknown, so we represent that with a variable x. The retail price would be 1.26x, which is 126% per flag.

Finally, if Fred paid $40 per flag, the actual retail price would be:

1.26($40)=$50.40.

With $10.40 of markup.

Answer:

  a) area will be 1/4 of the original

  b) 7 cm²

Step-by-step explanation:

Consider the equation for the area of a trapezoid:

  A = 1/2(b1 +b2)h

Now, halve each of the dimensions:

  A' = 1/2((1/2)b1 +(1/2)b2)((1/2)h)

  A' = (1/4)(1/2(b1 +b2)h) = 1/4A

The area is multiplied by the square of the scale factor: (1/2)² = 1/4.

__

The area of the smaller trapezoid will be ...

  A' = 1/4A = (1/4)(28 cm²) = 7 cm²

Answer:

24 is the number. The sum of its digits is 6.

Step-by-step explanation:

There are four two-digit numbers the product of whose digits is 8: 18, 24, 42, and 81. Of these numbers, 24 is four times the sum of its digits:

24 = 4 × 6 = 4 × (2 + 4)

A number that can only be divided by 1 or 0 is prime. A composite number is a number that can be divided by 0, 1, 2, etc. I couldn't really get the question that you were trying to type, but this is what I came up with.

Hope this helps and just remember you are loved!

Answer:

The third side is increasing at an approximate rate of about 0.444 meters per minute.

Step-by-step explanation:

We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.

Let the angle between the two given sides be θ and let the third side be c.

Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.

First, convert the degrees into radians:

\(\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}\)

Hence, dθ/dt = π/90.

From the Law of Cosines:

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

Since a = 13 and b = 19:

\(\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta\)

Simplify:

\(\displaystyle c^2 = 530 - 494\cos \theta\)

Take the derivative of both sides with respect to t:

\(\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right]\)

Implicitly differentiate:

\(\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}\)

We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:

\(\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}\)

Substitute:

\(\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)\)

Solve for dc/dt:

\(\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}\)

Evaluate. Hence:

\(\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}\)

The third side is increasing at an approximate rate of about 0.444 meters per minute.

9514 1404 393

Answer:

  0.444 m/min

Step-by-step explanation:

I find this kind of question to be answered easily by a graphing calculator.

The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...

  c = √(a² +b² -2ab·cos(C))

Since C is a function of time, its value in degrees can be written ...

  C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest

Using a=13, and b=19, the length of the third side is ...

  c(t) = √(13² +19² -2·13·19·cos(60° +2t°))

Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...

  0.443855627418 m/min ≈ 0.444 m/min

_____

Additional comment

At that time, the length of the third side is about 16.823 m.

__

c(t) reduces to √(530 -494cos(π/90·t +π/3))

Then the derivative is ...

  \(c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}\)

Answer:

I think it is p= $60

The y-intercept of the function is  -9,25

The function is given as:

\(y = -5(.8)^{x - 1} - 3\)

See attachment for the graph of the function

From the graph, we have the following highlights:

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Answer:

39

Step-by-step explanation: