An electrical resistor is rated at 4500 ohms ± 3%. Express this tolerance in ohms and state the
actual range of resistance.

A function assigns the values. The value a is 11.

A function assigns the value of each element of one set to the other specific element of another set.

The given logarithmic function can be solved as shown below.

[tex](\log(a-1))^2 =\log10\\\\(\log(a-1))^2 =1\\\\(\log(a-1)) =\sqrt1\\\\\log(a-1) = 1\\\\10^1 = a-1\\\\a = 11[/tex]

Hence, the value a is 11.

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There are 5 bags and each bag has 5 apples and total there are 25 apples , Option A is the correct answer.

A perfect square is a number which can be written as the product of an integer with itself.

It is given that Mark divided a basket of apples evenly into small bags.

Let there be n no. of bags and therefore n number of apples in each bag

Then the total number of apples will be

n * n

n²

The value of total number of apples should be a perfect square,

In the option given only 25 is the perfect square

Therefore the equation can be made as

n² = 25

n = 5

There are 5 bags and each bag has 5 apples and total there are 25 apples.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]

[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]

[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]

[tex]\qquad \tt \rightarrow \: - x + 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:6-x

Step-by-step explanation:

The solution is in the image

Answer:

$331.02

Step-by-step explanation:

compound interest formula

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

P = principal amount

r = rate decimal

n = number of times interest is compounded

t = time

A = 100 * (1 + .06/12)^(12*20)

A = 331.02

Answer:

1)  x + 96 = 90°

2)  x + 89 = 80°

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line.  Each pair of consecutive interior angles are supplementary (sum to 180°).

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 96)° + (x + 96)° = 180°

⇒ x + 96 + x + 96 = 180

⇒ 2x + 192 = 180

⇒ 2x + 192 - 192 = 180 - 192

⇒ 2x = -12

⇒ 2x ÷ 2 = -12 ÷ 2

⇒ x = -6

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 96 = -6 + 96 = 90°

⇒ x + 96 = 90°

To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 109)° + (x + 89)° = 180°

⇒ x + 109 + x + 89 = 180

⇒ 2x + 198 = 180

⇒ 2x + 198 - 198 = 180 - 198

⇒ 2x = -18

⇒ 2x ÷ 2 = -18 ÷ 2

⇒ x = -9

Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:

⇒ x + 89 = -9 + 89

⇒ x + 89 = 80°

Answer:

[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]

Step-by-step explanation:

Part 1 :

Part 2 :

1) The definitely true for the statement is b) P(-5) = 3.

2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x)

Given;

1) When the polynomial P(x) is divided by x+5, the remainder is 3.

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).

So, P(-5) = 3

Therefore, the definitely true for the statement is b) P(-5) = 3.

2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.

The complex roots always exist in conjugate pairs so,

3 + 4i and 3 - 4i

Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

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A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.

The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).

So the probability of selecting a green or purple counter is:

Probability = (Number of green counters + Number of purple counters) / Total number of counters

Probability = (7 + 1) / 11

Probability = 8/11

Therefore, the probability of selecting a green or purple counter is 8/11.

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Answer: B=16 and m=6

Step-by-step explanation:

in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.

Answer:

the next number is 47+ 16 =63

Answer:

m3+5

Step-by-step explanation:

m is miles

take the number of miles  multiply by3

take that answer add 5

The equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

A statement that relate two expressions with an equal sign is called an Equation.

It is given that

A cab company charges a $5 boarding

Charges for every mile is $3 per mile

Let x be the mile travelled

The cab's total charge is represented by y

then y = 3x + 5

Therefore the equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

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Answer:

3,36 in^2

Step-by-step explanation:

The geometric shape shown in image is called a trapezoid

to calculate the area of a trapezoid we use the following formula:

1/2*(a+b)*h (a and b are bases, h: height)

bases are 1.3 and 3.5 and height is 1.4

1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is

3,36 in^2

20% of the participants are girls and got a medal, and 33% of the girls got a medal.

First, we know that 40% of the participants were boys, so the other 60% were girls.

We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:

P = (0.4)*(0.5) = 0.2

So, 20% of the participants are boys and got a medal.

We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.

Then if the percentage of girls that got a medal is x (in decimal form), we must have that:

Q = (0.6)*(x) = 0.2

      x = 0.2/0.6 = 0.33

x = 0.33

This means that 33% of the girls got a medal.

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The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

The viewer represents the correct answers with x and the incorrect ones with y.

x+y = 20

for every correct answers 2 points;

and for every incorrect answers, -1 point

This can be written as

2x-y = 28

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

now

2x-y = 28

x+y = 20

On adding the equations

]3x = 48

x = 16

y = 4

This means that the contestant answered 16 questions correctly and 4 questions incorrectly

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

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Answer:

Step-by-step explanation:

Comment

The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.

Givens

Arc 1 = 94

Arc2 = d

interior angle = 75

Formula

(d + 94)/2 = interior angle/1

Solution

(d + 94)/2 = interior angle/1               Cross Multiply

1*(d + 94) = 75 *2                           Combine

d + 94 = 150                                        Subtract 94 from both sides

d + 94 - 94 = 150 - 94                         Combine

d = 56

Answer: d = 56

Answer:

sure how can I help you? please tell me

Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are given as follows:

Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.

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Answer:

P=2l+2W

if l=12 and W=8

then,

P=2L+2W

=2.18+2.8

=36+16

=52

Answer:

21 girls.

Step-by-step explanation:

50% of 42 students are girls.

So 42/2 = 21.

Therefore 21 of the students are girls.

Hope I helped

Answer:

Aprism =  483.246 yd2

Step-by-step explanation:

The surface area is the sum of the 2 circles areas and the rectangle area.

Ac1 = PI*r2

Ac1 = (3.14)*(11.4/2)2

Ac1 = 102.0186 yd2

Ac1 = Ac2 then

Ac2 = 102.0186 yd2

Now the perimeter of the circle is one the sides of the rectangle:

Pc = 2PI*r

Pc = 2*3.14*(11.4/2)

Pc = 35.796 yd

Now the area of the rectangle is:

Ar = 7.8yd*35.796yd

Ar = 279.2088 yd2

Then, the surface area of prism is:

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

A function is defined as a relation between the set of inputs having exactly one output each.

On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).

The domain is all real numbers.

The range is all real numbers.

If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.

The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).

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Answer:

A

Step-by-step explanation:

Answer:

Power of a quotient

The margin error of the confidence interval 0.87<p<0.93 is 0.03.

Given confidence interval 0.87<p<0.93.

We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random  sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.

Confidence interval is 0.87<p<0.93.

Width of the interval= 0.93-0.87

=0.06

=0.03

Hence the margin of error is equal to 0.03.

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Answer:

78.7

Step-by-step explanation:

To find the mean, we can do the sum of all scores divided by the total amount of scores.

We see that there are 7 scores of 70, and 70*7=490.

We see that there are 5 scores of 75, and 75*5=375.

We see that there are 4 scores of 80, and 80*4=320.

We see that there is 1 score of 85, and 85*1=85.

We see that there are 6 scores of 90, and 90*6=540.

Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]

Answer:

(i) 8b-32

(ii) 7z^3+12z^2-20z

(iii) –q+p

(iv) a+ab

(v) 8x^2y+8xy^2-4x^2-7y^2

(vi) 4y^2-3y

Step-by-step explanation:

The exponential equation with a base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

We start with:

[tex]f(x) = 6*(14)^x[/tex]

We want to rewrite this to:

[tex]f(x) = 6*(e^n)^x[/tex]

So we only need to find the value of n such that:

[tex]e^n = 14[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]

Then the exponential equation with base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

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The equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have:

Vertices of the hyperbola = (0, 5) and (0, -5)

Asymptotes: y = ±(5/12)x

The equations we have:

[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]

[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]

[tex]\rm \dfrac{x^{2}}{25}-\dfrac{y^{2}}{144}=1[/tex]

[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]

From the equation first:

[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]

The value of a and b are:

a = 12

b = 5

Vertices of the hyperbola = (0, b) and (0, -b)

Vertices of the hyperbola = (0, 5) and (0, -5)

Asymptotes: y = ±(b/a)x

Asymptotes: y = ±(5/12)x

Thus, the equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.

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Answer:

A

Step-by-step explanation:

Answer:

this is pretty easy we just replace the x with -1 so

(-1)^2+(-1)9+10

-1*-1=1

-1*9=-9

1+-9=-8

-8+10=2

f(-1)=2

Hope This Helps!!!

Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

The domain of the function is t ≥ 0

The greatest concentration of the medication is 5mg/L

Given that:

C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]

(a): The domain of the function

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is: t ≥ 0

(b) The greatest concentration of the medication

From the graph (see attachment), the maximum y-value is 5.

Hence, the greatest concentration of the medication is 5 mg/L

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Answer:

I think it's 80%

Step-by-step explanation:

Method 1: (40/50)*100 = 80%

Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%