Select the measurement most likely to be subject to random error. 1-Measuring temperature with a digital thermometer; 2-Measuring temperature with a mercury thermometer; 3-Measuring a distance in yards by pacing; 4-Determining the number of pennies in bags by dividing the weights of the filled bags by the legally defined weight of a penny.

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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Answer:

1.6

Step-by-step explanation:

7 and three tenths = 7 + 3/10 = 7.3

5 and seven tenths = 5 + 7/10 = 5.7

7.3-5.7 = 1.6 or can be written as 1 and six tenths, or 1 and three fifths.

Answer:

solve simultaneously

start by labeling them equation 1 and 2 then choose whether you want to make x or y the subject from knew of the equations

Answer:

A=-6

Step-by-step explanation:

Answer:

B, D, and E

Step-by-step explanation:

Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:

To be complement sum of angle must be 90°

But to be supplement sum of angle must be 180°

Step-by-step explanation:

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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A. The. part

B. The. whole

C. The. People

D. Benchmark. percent

The limit for this problem is given as follows:

\(\lim_{x \rightarrow 3} \frac{\sqrt{x + 2}}{x - 4} = -\sqrt{5}\)

The limit for this problem is defined as follows:

\(\lim_{x \rightarrow 3} \frac{\sqrt{x + 2}}{x - 4}\)

The point that is excluded from the domain of the function is given as follows:

x - 4 = 0 -> x = 4.

The limit is calculated at:

x = 3.

As the function is in fact defined at x = 3, we just obtain the numeric value of the function at x = 3, replacing each instance of x by 3, hence:

\(\lim_{x \rightarrow 3} \frac{\sqrt{x + 2}}{x - 4} = \frac{\sqrt{3 + 2}}{3 - 4} =  -\sqrt{5}\)

(positive divided by -1 is negative).

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To find:-

Answer:-

Here we need to find out the following limit ,

\(\implies \displaystyle \lim_{x\to 3}\dfrac{\sqrt{x+2}}{x-4} \\\)

We start by substituting x = 3 in the given limit as ,

\(\implies \displaystyle \dfrac{\sqrt{3+2}}{3-4} \\\)

Simplify,

\(\implies \displaystyle \dfrac{\sqrt{5}}{-1} \\\)

Multiply Numerator and Denominator by -1 ,

\(\implies \displaystyle -\sqrt{5}\\\)

Therefore,

\(\implies\underline{\underline{\green{ \displaystyle \lim_{x\to 3}\dfrac{\sqrt{x+2}}{x-4} =-\sqrt5}}} \\\)

and we are done!

Answer:

x=0

Step-by-step explanation:

:)

Answer:

\({ \tt{ \frac{3}{2}(6x + 2) = - 3(x - 1) }} \\ \\ { \tt{3(3x + 1) = - 3(x - 1)}} \\ { \tt{3x + 1 = - (x - 1)}} \\ { \tt{3x + 1 = - x + 1}} \\ { \tt{3x + x = 0}} \\ { \tt{x = 0}}\)

A box that contains two times as many cubes as a box that is 2 by 3 by 5 can have dimensions of 2 by 3 by 10.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A box that is 2 by 3 by 5 has a total of 2 x 3 x 5 = 30 cubes. To build a box that will hold twice as many cubes, we need to find the dimensions that will give a total of 60 cubes.

Let's assume the dimensions of the new box are x, y, and z. Then, we have:

xyz = 60

We can express one of the variables in terms of the other two.

z = 60 / (xy)

Substitute this in above equation.

xy60/xy=60

60=60

This is true for any values of x and y, as long as z is calculated as z = 60 / (x y).

There are infinitely many solutions for the dimensions that will give a box with a total of 60 cubes.

set of dimensions that satisfies the condition is x = 2, y = 3, and z = 10.

Hence, a box that contains two times as many cubes as a box that is 2 by 3 by 5 can have dimensions of 2 by 3 by 10.

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Answer:

B W(2,-4),X(6,-4)Y(6-10),Z(2,-10)

Step-by-step explanation:

i think dont get ur hopes ^

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

  y = (x +7)/(x -7)

Step-by-step explanation:

For dividing fractions like this, you can use the relation ...

  \(\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}=\dfrac{ad}{bc}\)

The simplification is done by cancelling common factors from numerator and denominator. In order to do that, we need to factor the numerator and denominator. We see that factors of 2, (x-2), and (x+7) will cancel.

  \(y=\dfrac{(2x^2+10x-28)(x+7)}{(x^2-49)(2x-4)}=\dfrac{2(x-2)(x+7)(x+7)}{2(x-2)(x+7)(x-7)}\\\\\boxed{y=\dfrac{x+7}{x-7}}\)

\(\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}\)

In order to simplify, by cross multiplication we can see that the factors of 2 i.e (x - 2) and (x + 7) will get cancelled.

\(:\implies\sf{y = \frac{(2 {x}^{2} + 10x - 28)(x + 7) }{( {x}^{2} - 49)(2x - 4)} } \\ \\ \\ :\implies\sf{ y = \frac{2(x - 2)(x + 7)(x + 7)}{2(x - 2)(x + 7)(x - 7)} } \\ \\ \\ :\implies\sf{y = \frac{ x+ 7}{x - 7} }\)

Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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The value of angle ABC is 26°

What is a value ?

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.

Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, justice, peace, and charity.

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.

to find the ∠ABC

we know ∠CAB = 64° and ∠BCA = 90°

let ∠ABC be x

x + 64 + 90 = 180

x = 180 - 64 - 90

  = 26°

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The area of the space available for onions is:n12 square feet - 0.12x square feet. number of onion bulbs Mark can plant is: (12 - 0.12x) / y

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

Mark has marked off a certain percentage of the 12 square feet to save for a tomato plant, which means the remaining space will be used for onions.

Let's say Mark marks off x% of the space for the tomato plant. That means he will have (100-x)% of the space for onions.

The area of the space reserved for the tomato plant is:

12 square feet x (x/100) = 0.12x square feet

The area of the space available for onions is:

12 square feet - 0.12x square feet

Let's say each onion bulb needs y square feet of room to grow. Mark can plant as many onion bulbs as can fit in the remaining space, which is:

(12 square feet - 0.12x square feet) / y

So the number of onion bulbs Mark can plant is:

(12 - 0.12x) / y.

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Answer:

b<7 or b>-1

Step-by-step explanation:

6b<42

b<7

4b+12>8

4b>-4

b>-1

Therefore, "b<7 or b>-1" is the correct answer

Answer:

Type 1 error :

D. Reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually 0.32.

Type 11 error :

C. Fail to reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually different from 0.32.

Step-by-step explanation:

A type 1 error is committed when a true null rejected. That is an incorrect rejection of a true null. Hence, by rejecting the claim that proportion ofbpop

Type 2 error is made when a false null is adopted. Here, we fail to reject a false null. In the scenario above, type 11 error will be made if we fail to reject the claim that proportion of People who write with their left hand is 0.32, when the proportion is correctly not 0.32

\(x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9\)

Answer:

x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

In my opinion it's 15 because calculators

Answer:

15

Step-by-step explanation:

10 can be written as 5 + 5

5 + 10

= 5 + 5 + 5

= 5 x ( 1 + 1 + 1 )

= 5 x 3

= 15

Answer:

10^2

Step-by-step explanation:

10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2

Answer:

100

Step-by-step explanation:

Hope it helps

Answer:

i donot know appp lado app

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

36:60:84

A     : B    : C

36° : 60° : 84°

A= 36°

B= 60°

C=84°

Step-by-step explanation:

3:5:7 =15

180÷15=12

3×12=36

36:x:y =180

5×12=60

36:60:y =180

7×12=84

36:60:84 =180

Answer: A=45  B=75  C=105

Step-by-step explanation:

3:5:7=180 degrees
   15=180
  15 divided by15=180 divided by 15
so,    1=12

so= 3:5:7 equal to (3*12)  (5*12)  (7*12)

A,B,C angles measures respectively = 36:60:84
  if you add them (A,B,C angles) we can obtain = 36:60:84=180    
  (sum of the measures of the angles of a triangle is 180 degrees)

Answer:

Ben ran at a speed of 240m/min and Sam ran at a speed of 200m/min So Ben is faster by a rate of 40/min

Step-by-step explanation:

Ben's miles per minutes

\( \frac{3600}{15} = 240\)

Sam's miles per minute

Given

Two tugboats that are a = 100 ft apart pull a barge, as shown. If the length of one cable is b = 206 ft and the length of the other is c = 235 ft, find the angle formed by the two cables. (Round your answer to the nearest degree.)​

we know that

The law of cosines states that

a^2=b^2+c^2-2(b)(c)cos(A)

In this problem we have

a=100 ft

b=206 ft

c=235 ft

A ----> is the angle formed by the two cables

substitute the given values in the formula

100^2=206^2+235^2-2(206)(235)cos(A)

Solve for cos(A)

2(206)(235)cos(A)=206^2+235^2-100^2

2(206)(235)cos(A)=87,661

cos(A)=0.9054

using a calculator

therefore

the answer is 25 degrees

The simplified expression for ( x - y ) ( x - y ) ( x - y ) is x³ - x²y - xy² + y³.

To simplify ( x - y ) ( x - y ) ( x - y ), we can expand the expression using the distributive property of multiplication. We can also simplify the expression by combining like terms.

In using the distributive property of multiplication, we multiply each term in the first set of parentheses by each term in the second set of parentheses. This gives us:( x - y ) ( x - y ) ( x - y ) = ( x(x - y) - y(x - y) ) ( x - y )= ( x² - xy - xy + y² ) ( x - y )= ( x² - 2xy + y² ) ( x - y )

Now we can further simplify the expression by combining like terms. We can use the difference of squares formula to simplify the second set of parentheses.( x² - 2xy + y² ) ( x - y ) = ( x - y ) ( x - y )²= ( x - y ) ( x² - 2xy + y² )= x³ - x²y - 2xy² + xy² - xy² + y³= x³ - x²y - xy² + y³

Therefore, the simplified expression is x³ - x²y - xy² + y³.

Summary: To simplify ( x - y ) ( x - y ) ( x - y ), we expand the expression using the distributive property of multiplication. We simplify the expression by combining like terms. We use the difference of squares formula to simplify the second set of parentheses. Finally, we simplify the expression further by combining like terms. The simplified expression is x³ - x²y - xy² + y³.

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