1/2×-7=1/3(×-12) solve​

Answer:

139°

Step-by-step explanation:

18°+23°+?= 180°{sum of angles on a triangle}

41°+?° = 180°

?° =180-41=139°

The correct answer is Option 3 (0,2). The medians of a triangle intersect at the midpoint of the opposite side of the triangle.

Triangle is a three-sided geometric shape with three angles and three vertices. Triangles can be classified into different types based on the lengths of their sides and the angles between them. The three most commonly referred to types include the equilateral, isosceles and scalene triangle. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length. A scalene triangle has no equal sides or angles. All three types of triangles have interior angles that add up to 180 degrees and all three sides must be connected. All triangles are two-dimensional shapes, meaning they have no thickness or depth.

In triangle ABC, the opposite side is the line segment BC, which has endpoints at (-3,2) and (1,2). The midpoint of this line segment is (0,2).

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Complete question :

It is desired to check the calibration of a scale by weighing a standard 10 g weight 100 times. Let µ be the population mean reading on the scale, so that the scale is in calibration if µ = 10. A test is made of the hypotheses H0:µ = 10 versus H1:µ ≠ 10. Consider three possible conclusions: (i) The scale is in calibration, (ii) The scale is out of calibration, (iii) The scale might be in calibration.

Which of the three conclusions is best ifH0 is rejected?

Answer:

The scale is out of calibration

Step-by-step explanation:

The null hypothesis ; H0

H0 : μ = 10 ; if this hold true, then the scale is in calibration

Alternative hypothesis ; H1

H1 : μ ≠ 10 ; if this holds true, then the scale is out of calibration

If the Null hypothesis, H0 is rejected, it means that, there is significant evidence to support the alternative hypothesis ; that the scale is out of calibration.

Hence, the best conclusion is that, the scale is out of calibration.

Answer:

2(10^.5)

Step-by-step explanation:

d = ((x2 - x1)^2 + (y2 - y1)^2)^0.5

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

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Answer:

I think the solution is x=84 if this is correct can u mark me brainliest

Answer:

Step-by-step explanation:

This problem can be solved by using the logarithm function.

Isolate the term of x from one side of the equation.

First, you divide by -6 from both sides.

\(\Longrightarrow: \sf{\dfrac{-6\log _3(x-3)}{-6}=\dfrac{-24}{-6}}\)

Solve.

Divide the numbers from left to right.

-24/-6=4

Rewrite the problem down.

\(\Longrightarrow: \sf{\log _3(x-3)=4}\)

x-3=81

Add by 3 from both sides.

\(\Longrightarrow:\sf{x-3+3=81+3}\)

Solve.

Add the numbers from left to right.

81+3=84

\(\Longrightarrow: \boxed{\sf{x=84}}\)

I hope this helps you! Let me know if my answer is wrong or not.

The probability that it is British is 0.6164 if the Venn diagram shows the information about a stamp collection. f = 100 stamps in the collection A = stamps in the 20th century B = British stamps A B. X(X - 6) х 2x + 32 28 A stamp is chosen at random.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

f = 100 stamps in the collection

A = stamps in the 20th century

B = British stamps

We can make a linear equation to solve for x as the total stamps are 100 in the collection.

\(\rm x(x-6)+x+2x+32= 100\\\\\rm x^2-6x+x+2x+32 = 100\\\\\rm x^2-3x-68 = 0\)

After solving x = 9.88, or x = -6.88

Probability can't be negative so neglecting the negative ones

x = 9.88

The probability that it is British:

\(=\rm \frac{x +2x + 32}{100}\)  

\(=\rm \frac{9.88 +2(9.88) + 32}{100}\)

= 61.64/100

= 0.6164

Thus, the probability that it is British is 0.6164 if the Venn diagram shows the information about a stamp collection. f = 100 stamps in the collection A = stamps in the 20th century B = British stamps A B. X(X - 6) х 2x + 32 28 A stamp is chosen at random.

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Answer:

76.665

Step-by-step explanation:

Given that,

cos α = 0.93, Sin θ =0.26 and tanβ = 0.84

We need to find the value of α, β and θ

\(\alpha =\cos^{-1}(0.93)\\\\=21.565\\\\\beta =\tan^{-1}(0.84)\\\\=40.030\\\\\theta=\sin^{-1}(0.26)\\\\=15.07\)

So,

\(\alpha +\beta +\theta=21.565+40.03+15.07\\\\=76.665\)

Hence, the final answer is 76.665.

Answer:

Yes it is a proportional relationship becasue the line is straight.

Step-by-step explanation:

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

x=−3

Step-by-step explanation:

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

1000 and 3000

Step-by-step explanation:

Answer:

5 sec

Step-by-step explanation:

Hit the water, means h = 0

Solve -16t^2 + 68t +60 =0

4t^2 - 17t - 15 = 0

(4t + 3)(t - 5) = 0

so t = 5 sec

Answer:

the answer is $15

Step-by-step explanation:

0.20 x 75 = 15

The spreadsheet is missing, so i have attached it.

Answer:

Option A - $295

Step-by-step explanation:

From the spreadsheet, net pay = $2300 and interest earned on savings = $20

Therefore, her total income = $2300 + $20 = $2320

Now,from the spreadsheet, total expenses = 800 + 120 + 90 + 45 + 95 + 80 + 275 + 520 = $2025

Now, net cash flow = Total income - Total expenses

Net cash flow = $2320 - $2025

Net cash flow = $295

Answer:

a. 295

Step-by-step explanation:

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

Plot these points

(-3,0)

(-5,0)

(-4,1)

(-2,-3)

(-6,-3)

Step-by-step explanation:

Let find the zeros of the equation.

We can factor this equation.

Factor out the -1.

\( - 1( {x}^{2} + 8x + 15)\)

Factor using AC method

\( - 1(x + 3)(x + 5)\)

Set all the terms equal to zero.

\(x + 3 = 0\)

\(x + 5 = 0\)

\(x = - 3\)

\(x = - 5\)

So our x intercepts are -3,0 and -5,0.

To find our vertex, apply the -b/2a.

\( \frac{8}{ - 2} = - 4\)

Then

Substitute-4 for x.

\(y = - {4}^{2} - 8( - 4) - 15 = 1\)

So our vertex is at (-4,1).

Find some other points like -2 and -6.

To find -2, substitute-2 into the quadratic.

\(y = - ( { - 2}^{2}) - 8( - 2) - 15 = - 3\)

So -2,-3.

Since y=-4 is the axis of symmetry

-6,-3

The 5 points which satisfies the quadratic equation y = −x² − 8x − 15 is

( -5 , 0 ) ( -1 , -8 ) , ( -2 , -3 ) , ( 4 , 1 ) , ( -3 , 0 ) and the vertex point is ( 4 , 1 )

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

y = −x² − 8x − 15

On simplifying the equation , we get

y = -1 ( x² + 8x + 15 )

On factorizing the equation , we get

y = -1 ( ( x + 5 ) ( x + 3 )

So , the 2 values for x is -5 , -3

So , the two points are ( -5 , 0 ) and ( -3 , 0 )

The vertex will be -b/2a

Substituting the values in the equation , we get

The vertex = -8/2 = -4

So , when x = -4

y =  -1 ( ( x + 5 ) ( x + 3 )

y = -1 ( 1 x -1 )

y = 1

So , the vertex is at the point ( 4 , 1 )

Now , when x = -1

y = -1 ( ( x + 5 ) ( x + 3 )

y = -1 ( 4 x 2 )

y = -8

So , the point is ( -1 , -8 )

Now , when x = -2

y = -1 ( ( x + 5 ) ( x + 3 )

y = -1 ( 3 x 1 )

y = -3

So , the point is ( -2 , -3 )

Hence ,

The 5 points which satisfies the quadratic equation y = −x² − 8x − 15 is

( -5 , 0 ) ( -1 , -8 ) , ( -2 , -3 ) , ( 4 , 1 ) , ( -3 , 0 ) and the vertex point is ( 4 , 1 )

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There are 2 pints in 1 quart, and 4 cups is equal to 1 quart, so we can convert 4 cups to pints using the following steps:

1 quart = 2 pints

1 cup = 1/4 quart

4 cups = 4 x (1/4) quart = 1 quart

Therefore, 4 cups is equal to 2 pints.

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\(\textcolor{cyan}{\small\textit{If you have any further questions, feel free to ask!}}\)

Answer:

x = 14

Step-by-step explanation:

→ Set up an equation

4x + 15 + 39 = 110

→ Simplify

4x + 54 = 110

→ Minus 54 from both sides

4x = 56

→ Divide both sides by 3

x = 14

Answer:

D. All the above are correct

Step-by-step explanation:

An isocost line will be shifted further away from the origin if the total cost increases, if the price of both inputs increases or there is an advance in technology.

An isocost line can be defined as the graphical representation of various combinations of two inputs factors (labor,L and capital, K) which the firm can afford or purchase with a given amount of money.

An isocost line can be expressed mathematically as:

C = w L + r K

Where,

C = cost of production

w = price of labor or wages

L = units of labor

r = price of capital or interest rate

K =units of capital

Isocost is used to determine what combination of factor inputs the firm will choose for production process.

An iso-cost line will be shifted further away from the origin'' All of the above are correct".

An iso-cost line will shift either because of a change in total outlay or a change in factor prices.

A change in total outlay will cause a parallel shift in the iso-cost line, as there will be no change in its slope, factor prices being constant.

An iso-cost line will be shifted further away from the origin if the total cost increases if the price of both inputs increases or there is an advance in technology.

An iso-cost line can be defined as the graphical representation of various combinations of two inputs factors (labor, L and capital, K) which the firm can afford or purchase with a given amount of money.

Each iso-cost curve represents a fixed level of costs and the isoquant represents a fixed level of output.

Therefore, tracing a line through these set of points represents what combination of labor and capital will be used for a fixed level of costs or output.

The points further away from the origin represent higher levels of costs or output. An iso-cost line can be expressed mathematically as:

\(C = w L + r K\)

Where, C = cost of production

w = price of labor or wages

L = units of labor

r = price of capital or interest rate

K =units of capital

Iso-cost is used to determine what combination of factor inputs the firm will choose for the production process.

Hence, An iso-cost line will be shifted further away from the origin'' All of the above are correct".

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Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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Answer:

Step-by-step explanation:

Volume of the ball (spherical in nature) Vb = 4/3πrb³

Volume of the hole Vh = 4/3πrh³

rb is the radius of the ball

rh is the radius of the hole

If a ball of radius 17 has a round hole of radius 7 drilled through its center, the volume of the resulting solid will be expressed as:

V = Vb - Vh

V = 4/3πrb³ - 4/3πrh³

factor out the like terms;

V = 4/3π(rb³-rh³)

Given

rb = 17

rh = 7

V = 4/3π(17³-7³)

V = 4/3π(4913-343)

V = 4/3π(4570)

V = (4π*4570)/3

V = 57,399.2/3

V = 19,133.067

Hence the volume of the resulting solid is 19,133.067

The standard deviation of the distribution is given as follows:

\(\sigma = 17.2\)

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

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

The mean of the distribution of IQ scores is given as follows:

\(\mu = 100\)

X = 140 is the 99th percentile, as approximately 1% of the population have IQ scores above this limit, hence when X = 140, Z = 2.327, meaning that the standard deviation is obtained as follows:

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

\(2.327 = \frac{140 - 100}{\sigma}\)

\(2.327\sigma = 40\)

\(\sigma = \frac{40}{2.327}\)

\(\sigma = 17.2\)

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\(a = 9\)

\(b = 12\)

\(c = \sqrt{ {a}^{2} + {b}^{2} } = \sqrt{ {9}^{2} + {12}^{2} } = \sqrt{81 + 144} = \sqrt{225} = 15\)

\(p = a + b + c = 9 + 12 + 15 = 36\)

Answer: 36.

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.