Question What is the value of the expression? 75÷5−[(9−7)×3]×2 Enter your answer in the box.

Answer:

11° 33'

Step-by-step explanation:

[tex]21' = \left(\dfrac{21}{60}\right)^\circ = \left(\dfrac{7}{20}\right)^\circ \\50^\circ 21' = 50 \dfrac{21}{60}\; degrees\\\\38^\circ 48' = 38 \dfrac{48}{60} \;degrees[/tex]

Break
[tex]50 \dfrac{21}{60} = 49 + 1 \dfrac{21}{60}\\[/tex]

[tex]1 \dfrac{21}{60} = \dfrac{1 \times 60 + 21}{60} = \dfrac{81}{60}[/tex]

Therefore
[tex]50^\circ21' - 38^\circ48' = 49\dfrac{81}{60} - 38\dfrac{48}{60}[/tex]

Subtract the whole numbers:
49 - 38 = 11

Subtract the fractions:
[tex]\dfrac{81}{60} - \dfrac{48}{60} = \dfrac{33}{60} = 33'[/tex]

So

50°21' - 38°48' = 11° 33'

We expect that, on average, 1 out of 25 patients calling in claiming to have the flu will actually have the flu.

According to the nurse's observation, there is a 4% chance that a patient who calls the medical advice line and claims to have the flu truly has.

As a result, we anticipate that 4 out of every 25 people who phone in will truly have the flu.

To figure this out, we can use the formula below:

Probability of having the flu multiplied by the total number of patients equals the anticipated number of flu patients.

Estimated number of influenza patients = 0.04 times 25

Expected number of influenza patients is one.

Hence, on average, we anticipate that 1 out of every 25 individuals who call in and claim to have the flu will truly have it.

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Answer:

Therefore, the total value of Mary's investment after two years is $700.

Step-by-step explanation:

To calculate the total value of Mary's investment after two years, we need to calculate the value of the investment after the first year, and then use that value to calculate the value after the second year.

In the first year, the value of the investment increases by 8%, so the value after the first year is:

Value after first year = $600 + 8% of $600

Value after first year = $600 + 0.08 * $600

Value after first year = $648

In the second year, the value of the investment increases by another 8%, so the value after the second year is:

Value after second year = Value after first year + 8% of Value after first year

Value after second year = $648 + 0.08 * $648

Value after second year = $699.84

Rounding to the nearest dollar, the total value of Mary's investment after two years is:

Total value after two years = $700

We have shown that the product of two rational numbers is rational.

A number system is defined as a system of writing to express numbers.

Let a and b be two rational numbers, such that:

a = p/q

b = r/s

where p, q, r, and s are integers and q, s are non-zero.

We need to show that the product ab is also a rational number.

We have:

ab = (p/q) x (r/s)

= (p x r) / (q x s)

Since p, q, r, and s are all integers,

ab = m/n

where m = p x r and n = q x s.

Since both m and n are integers and n is non-zero ,we can conclude that ab is a rational number.

Therefore, we have shown that the product of two rational numbers is rational.

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Answer:

(0.0301, 0.1733)

Step-by-step explanation:

[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]

Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733

f(x) is discontinuous.

Since LHS ≠ RHS ≠ f(x).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

here, we have,

We have,

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Now,

A x = 1

LHS of f(x) = lim f((h - 1)) =  (h - 1 - 1) = 0 -2 = -2

RHS of f(x) = lim  f(h + 1) =  (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1

f(1) = x + 1 = 1 + 1 = 2

We see that,

LHS ≠ RHS ≠ f(x)

So,

f(x) is not continuous, it is discontinuous.

Thus,

f(x) is discontinuous.

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The complete question.

Show that the following functions are continuous or discontinuous at x = 1.

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is [tex]\bar x\pm t\frac{s}{\sqrt{n}}[/tex].

Where, [tex]\bar x[/tex] is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

[tex]\bar x[/tex] =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

[tex]\bar x\pm tS_c[/tex]

[tex]\bar x+ tS_c[/tex] =1.267-2.7564(0.2246) =0.6479

[tex]\bar x- tS_c[/tex] =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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Answer: $3,700 or $90,650

Step-by-step explanation:

Answer:

3,700

Step-by-step explanation:

i thibk thisisthay answer

The percentage error of the student's estimated mass is 2.15%.

The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.

The estimated mass of the student = 82.0 kg

The actual mass of the student = 83.8 kg

Absolute error = Actual Value - Estimated Value

= 1.8 kg (83.8 - 82.0)

Percentage error = Actual Value - Estimated Value /Actual Value x 100

= 2.15% (1.8/83.8 x 100)

Thus, we can conclude that the student's estimate contains a 2.15% error.

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Answer:

the efficiency of the generator is 81.82%.

Step-by-step explanation:

The efficiency of a generator is defined as the ratio of the electrical power output to the mechanical power input. In this problem, the electrical power output is given as 90 hp, and the mechanical power input is the power supplied by the engine, which is 110 hp. Therefore, the efficiency of the generator can be calculated as follows:

Efficiency = Electrical power output / Mechanical power input

Efficiency = 90 hp / 110 hp

Simplifying the fraction, we get:

Efficiency = 0.8182

To convert this decimal to a percentage, we multiply by 100:

Efficiency = 0.8182 * 100

Rounding to two decimal places, we get:

Efficiency = 81.82%

Therefore, the efficiency of the generator is 81.82%.

Answer:

x = 54

Step-by-step explanation:

See picture below :)

Given the Figure shown below is, ΔABC~ΔAXY if so, 1.67 is the scale factor between the two triangles.

The ratio between the scale of an original thing and a new object that is a representation of it but has a different size is known as a scale factor (bigger or smaller).

Consider two comparable squares as an illustration. One has a side length of 2 inches, while the other has a side length of 4 inches. This results in a scale factor of 1: 2 from the small square to the huge square. The scale factor between these two comparable squares is 1: 2, or tiny square to huge square.

Given that,

12 / 20 = 17 / x

or, 12 x = 340

or, x = 28.33

on the other hand,

25 / 15 = 1.66

20 / 12 = 1.66

28.33 / 17 = 1.66

now, scale factor = 1.67

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Answer:

Step-by-step explanation:

To solve for b, we can use the law of sines, which states that in any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Here, we are given B = 150°, C = 20°, and c = 21 inches. We can solve for the remaining angle A by using the fact that the angles of a triangle add up to 180°:

A + B + C = 180°

A = 180° - B - C

A = 180° - 150° - 20°

A = 10°

Now we can use the law of sines to solve for b:

a/sin(A) = b/sin(B)

a = c * sin(A)/sin(C) = 21 * sin(10°)/sin(20°)

b = a * sin(B)/sin(A) = 21 * sin(10°)/sin(20°) * sin(150°)/sin(10°)

b = 21 * sin(150°)/sin(20°)

Using a calculator, we get:

b ≈ 41 inches (rounded to the nearest whole number)

Therefore, the length of side b is approximately 41 inches.

The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,

⇒ 1/3

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.

Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,

⇒ 1/3

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The probability that now the card is indeed a diamond or a face card is [tex]\frac{11}{26}[/tex].

The probability that any random event will occur is referred to as probability. This expression is used to calculate the likelihood that a given event will occur. When we fling a coin into the air, as an illustration. Probability: P(A) = f / N calculates the probability that an event will take place. Ratios and probability are related, but the former determines the latter. When calculating the likelihood of an event, it is necessary to know the probability of that event.

When we find the probability, we obtain:

A typical deck of cards contains 52 cards. There are 12 face cards, known as the Kings, Queens, and Jacks, because there are four suits. There are a total of 13 diamonds, of which 3 are previously counted face cards. Hence, there are 10 diamonds that are faceless.

So, total Diamond & face card =22

Probability =[tex]\frac{22}{52}[/tex]=[tex]\frac{11}{26}[/tex].

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The question you have indicated appears incomplete. However, here is a very similar example that uses the same logic and principles of probability and proportion. In this case, the proof is given below.

a.

Given: f(x) = 2(x+2)/5 , 0 <x< 1

Calculating P(0 <X< 1)

P(0 <X< 1) = ∫ f(x) dx {0.1}

Substitute 2(x+2)/5 for f(x)

P(0 <X< 1) = ∫ 2(x+2)/5 dx {0.1}

P(0 <X< 1) = 2/5 ∫(x+2) dx {0.1}

Integrate with respect to x

P(0 <X< 1) = 2/5 (x²/2+2x) {0.1}

P(0 <X< 1) = 2/5 (1²/2+2(1))

P(0 <X< 1) = 2/5 (½+2)

P(0 <X< 1) = 2/5 * 5/2

P(0 <X< 1) = 1 ----- Proved

b.

Here we're to solve for P(¼<X< ½)

P(¼<X< ½) = ∫ f(x) dx {¼,½}

Substitute 2(x+2)/5 for f(x)

P(¼<X< ½) = ∫ 2(x+2)/5 dx {¼,½}

P(¼<X< ½) = 2/5 ∫(x+2) dx {¼,½}

P(¼<X< ½) = 2/5 (x²/2+2x) {¼,½}

P(¼<X< ½) = 2/5 [ (½²/2+2(½)) - (¼²/2+2(¼))]

P(¼<X< ½) = 2/5 [(⅛+1)-(1/32 + ½)]

P(¼<X< ½) = 0.2375

The probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation is 0.2375

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Full Question:

The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function f(x) = 2(x+2)/5 , 0 <x< 1, 0, elsewhere.

(a) Show that P(0 <X< 1) = 1.

(b) Find the probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation.

[tex]\textit{Partial Variation} \\\\ y = k_ox+k_1\hspace{5em}\textit{"y" varies partly with a constant and directly with "x"} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{"D" varies partly with a constant and directly with "V"}}{D=k_oV+k_1}\qquad \textit{we know that} \begin{cases} V=40\\ D=150\\[-0.5em] \hrulefill\\ V=54\\ D=192 \end{cases}[/tex]

[tex]\boxed{\begin{array}{llll} 150=40k_o+k_1\\\\ 192=54k_o+k_1 \end{array}}\qquad \stackrel{ \textit{using elimination method} }{\begin{array}{llll} -150=-40k_o-k_1\\\\ ~~ 192= ~~ 54k_o+k_1\\\cline{1-1} ~~ 42~= ~~ 14k_o+0 \end{array} }\qquad \implies 42=14k_o \\\\\\ \cfrac{42}{14}=k_o\implies \boxed{3=k_o}\hspace{5em}\stackrel{\textit{substituting on the 1st equation}}{150=40(3)+k_1}[/tex]

[tex]\cfrac{150}{40(3)}=k_1\implies \boxed{\cfrac{5}{4}=k_1}\hspace{5em} {\Large \begin{array}{llll} D=3V+\cfrac{5}{4} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{when V=73, what is "D"?}\qquad D=3(73)+\cfrac{5}{4}\implies D=\cfrac{881}{4}\implies D=220\frac{1}{4}[/tex]

Answer:

43% * 258 = 110.94 (£110.94 is 43% of £258) 258 + 110.94 = 368.94

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3x + 7y)(3x - 7y)  FOIL

9x² -49y²   yes, this is difference of two squares

(2x - 7y)(2x - 7y)   FOIL

4x² -14x -14x +49y²

4x² -28x + 49y²   not difference of two squares

9x²(5x - 7)    Distribute the 9x²

45x³ - 63x²   not difference of two squares because one term is cubed

(6x - 4y)²    Distribute the square term

36x² - 16y²   yes, difference of two squares

Using the vertical line test we conclude that y is not a function of x.

When we have the graph of a relation, the vertical line test says that if we draw a vertical line over the graph and it intercepts the graph in more than one point, then the graph does not represent a function.

Here we have the graph of a circle, and there are multiple lines that intercept the graph twice (for example the line x = 0)

So we can conclude that this is not a function, thus, the correct option is A.

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The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

Some points about standard deviation using Empirical Formula:

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The Volume of Solid is 2,773.66 inch³ and Surface Area is

2,552.82 inch².

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given:

Cylinder: Height = 30 inch, Radius = 5 inch

Semi sphere: radius = 5 inch

Cone: Height = 6 inch, radius = 5 inch, l= √r² + h² = 7.81 inch

Now, The Volume solid

= Volume of Semi sphere  + Volume of Cylinder + Vol. of Cone

= 2/3 πr³ + πr²H + 1/3 πr²h

= πr² (2/3 r + H + 1/3 h)

= 3.14 x 5 x 5 (2/3(5) + 30 + 1/3 (6))

= 78.5 x ( 10/ 3 + 30 + 2)

= 2,773.66 inch³

Now, the Surface Area of Solid

= SA (Cylinder+ S. Sphere + Cone)

= πr²H + 2πr² + 1/3 πrl

= πr (rH + 2r + 1/3l)

= 3.14 x 5 (150 + 10 + 2.60)

= 2,552.82 inch²

Now, the model is increased by 8 times then the dimensions are:

Cylinder: Height = 240 inch, Radius = 40 inch

Semi sphere: radius = 40 inch

Cone: Height = 48 inch, radius = 40 inch, l= √r² + h² = 62.48 inch

and, Now, The Volume solid after dilation

= Volume of Semi sphere  + Volume of Cylinder + Vol. of Cone

= 2/3 πr³ + πr²H + 1/3 πr²h

= πr² (2/3 r + H + 1/3 h)

= 3.14 x 40 x 40 (2/3(40) + 240 + 1/3 (48))

= 78.5 x ( 10/ 3 + 30 + 2)

= 1,420,117.33 inch³

Now, the Surface Area of Solid

= SA (Cylinder+ S. Sphere + Cone)

= πr²H + 2πr² + 1/3 πrl

= πr (rH + 2r + 1/3l)

= 3.14 x 5 (1200 + 80 + 20.82)

= 163, 382. 992 inch²

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True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.

A confidence intervals bar chart (shown as red lines)

In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.

According to the definition the statement is true.

True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.

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The cost of the burger and the cost of an order of fries to Lynn would be :

From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:

4h + 5f = 20

10h + 7f = 41.20

Using substitution, we can express h in form of f to be :

4h + 5f = 20

4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20

6 f + 2 . 40 + 5 f = 20

11 f = 17. 60

f = $ 1. 60

We can then find the cost of hamburgers using the first equation :

4h + 5f = 20

4h + 5 ( 1. 60 ) = 20

4h + 8 = 20

4h = 12

h = $ 3

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[-1.5, 3.5] and [-2, infty) are the range and domain of the equation.

Quadratic function are functions that have a leading degree of 2.

The domain of the function are values that lies along the x-axis of the graph. Hence the domain of the curve will be [-1.5, 3.5]

The range of the function are values that lies along the y-axis of the graph. Hence the domain of the curve will be [-2, infty)

Hence the range and domain of the graph are [-1.5, 3.5] and [-2, infty)

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The difference quotient expression for the given function is

[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]

The expression in single-variable calculus is usually referred to as the difference quotient.

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

When taken to the limit as h gets closer to zero, h frac f(x+h)-f(x)h, which gives the derivative of the function f.

The slope of a secant line passing through the curve of f(x) is measured by the difference quotient.

Consider the difference quotient formula,

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

Evaluate the function at x = x + h

replace the variable x with (x + h) in the given expression

[tex]f(x+h)=\sqrt{(x+h)^2-1}[/tex]

simplify the result ,

[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]

find the components of the definition,

[tex]f(x+h)=\sqrt{(x+h+1)(x+h-1)}[/tex]

[tex]f(x)=\sqrt{(x+1)(x-1)}[/tex]

plug in the components,

[tex]\frac{f(x+h)-f(x)}{h} =\frac{\sqrt{(x+h+1)(x+h-1)}-\sqrt{(x+1)(x-1)} }{h}[/tex]

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The fraction of May's property that is left is 7/15.

A fraction is a value derived in such a way that it is a part of a given initial value. An example is one third of 12 is 4. In this case, 4 is a fraction of 12.

Considering the given question, we have;

let the total property of May be represented by 1, so that

fraction left after giving 1/5 to her son = 1 - 1/5

                             = (5 - 1)/ 5

                             = 4/ 5

The fraction left after giving 1/5 of her property to her son is 4/ 5.

So that;

the fraction left after she gave 1/3 to her daughter = 4/ 5 - 1/ 3

                                               = (12 - 5)/ 15

                                               = 7/ 15

Therefore, the fraction of her property left is 7/ 15.

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Answer:

true

Step-by-step explanation:

cause I’ve done this before

the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.

How we solved?

To determine the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8}, we first need to identify which numbers in the set are prime.

The prime numbers in the set are 5 and 7, so the non-prime numbers are 4, 6, and 8.

The total number of cards in the set is 5.

Therefore, the probability of selecting a non-prime card is:

P(not prime) = number of non-prime cards / total number of cards

P(not prime) = 3 / 5

P(not prime) = 0.6 or 60%

So the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.

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