8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?

Answers

Answer 1

Answer:

GH¢. 18098.46

Step-by-step explanation:

Let the first investment giving 12% interest per annum be Bank A

Let the 2nd investment giving 10% per annum be bank B

Let the first amount invested be

GH¢. X and let the second amount invested be GH¢. X + 580

Thus; In bank A;

Principal amount in first = GH¢. x

rate = 12 %

time = 1 year

Formula for simple interest = PRT/100

Where P is principal, R is rate and T is time.

So, interest in his investment = 12X/100 = 0.12X

while in bank B;

principal amount = GH¢. X + 580

rate = 14%

time = 1 yr

So, interest in his investment = [(X + 580) × 14]/100

= 0.14(X + 580)

So, total accumulated interest is;

0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2

Now, we are given accumulated interest = GH¢. 2,358.60

Thus;

2358.60 = (0.26X + 81.2)

2358.6 - 81.2 = 0.26X

X = 2277.4/0.26

X = 8759.23

So,

first amount invested = GH¢. 8759.23

Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23

Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46


Related Questions



Are You Ready for More?: Two raised to the 12th power is equal to 4,096. How many other

whole numbers can you raise to a power and get 4,096? Explain or show your reasoning.

(1 Point)

2^12 = 4096

Answers

Answer:

4, 8, 16,64 and 4096.

Step-by-step explanation:

We are already given: [tex]4096=2^{12}[/tex]

To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.

Product Rule of Indices: [tex]a^{xy}=(a^x)^y[/tex]

Now 12 can be factored in the following ways where one of the terms must be a perfect square:

12=2 X 612 =6 X 212 =3 X 412 =4 X 312=1 X 12

[tex]2^{12}=(2^2)^6=4^6\\\\2^{12}=(2^6)^2=64^2\\\\2^{12}=(2^4)^3=16^3\\\\2^{12}=(2^3)^4=(8^2)^2=8^{2*2}=8^4\\\\2^{12}=(2^{12})^1=4096^1 $(This is the trivial case)[/tex]

Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.

Which numbers are solutions of the inequality below? (Select all that apply.)
x − 2 < −8

a) 6

b) −6

c) 4

d) −8

Answers

Answer:

d) −8

Step-by-step explanation:

x − 2+2 < −8+2

x < -6

The only number less than -6 is -8

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 61% C: Scores below the top 39% and above the bottom 21% D: Scores below the top 79% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 67.7 and a standard deviation of 7.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answers

Answer:

The minimum score required for an A grade is 77.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

In this question, we have that:

[tex]\mu = 67.7, \sigma = 7.8[/tex]

Find the minimum score required for an A grade.

Top 12% of scores get an A.

100-12 = 88th percentile.

The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.175 = \frac{X - 67.7}{7.8}[/tex]

[tex]X - 67.7 = 7.8*1.175[/tex]

[tex]X = 76.865[/tex]

Rounding to the nearest whole number:

The minimum score required for an A grade is 77.

Help asap giving branlist!!!

Answers

Answer:

B

Step-by-step explanation:

Let's arrange it into slope-intercept form.

2x - y = 4

y = 2x - 4

We are looking for a line with slope of 2 and y-intercept -4. This line is Line B.

Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.

Answers

Answer:

  4u²

Step-by-step explanation:

  [tex]\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}[/tex]

Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.

What is the y-intercept of a line that has a slope of -3 and passes through point (0, -7)?

Answers

Answer:

Step-by-step explanation:

line equation:  y=mx + C

substitute given values

-7 = -3*0 + C

C=y= -7      ANS

A laptop producing company also produces laptop batteries, and claims that the batteries
it produces power a laptop for about 4:00 hours. But, you doubted the claim and collected
data from 500 laptop users of the same brand and battery, and you found out the battery
powers the laptop for about 3:00 hours and 30 minutes. Considering an alpha of 0.05,
prove the claim of the company is true or false or show whether you accept the
company’s claim or reject it? Please also write H0 and Ha statements for testing your
hypothesis

Answers

Answer:

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]

Step-by-step explanation:

The question is incomplete: To test this claim a sample or population standard deviation is needed.

We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.

NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=500-1=499[/tex]

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t<-5.5902)=0[/tex]

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

Write the standard form of the line that passes through the given points. Inclide your work in the final answer. Type your answer in the box provided or use the upload option to submit your solution. (4,7) and (0,7)

Answers

Answer:

y=7

Step-by-step explanation:

Slope: 7-7/4-0=0

Point: (0,7)

pt/slope form:

y-7=(0)(x-0)

y=7

1. O perímetro de um quadrado é 20 cm. Determine sua diagonal. 1 ponto a) 2 √5 cm b) 20√2 cm c) 5√2 cm d) 2√10 cm

Answers

Answer:

c) 5√2 cm

Step-by-step explanation:

A square with side length l has a perimeter given by the following equation:

P = 4l.

In this question:

P = 20

So the side length is:

4l = 20

l = 20/4

l = 5

Diagonal

The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.

[tex]d^{2} = l^{2} + l^{2}[/tex]

[tex]d^{2} = 5^{2} + 5^{2}[/tex]

[tex]d^{2} = 50[/tex]

[tex]d = \pm \sqrt{50}[/tex]

Lenght is a positive meausre, so

[tex]d = \sqrt{50}[/tex]

[tex]d = \sqrt{2 \times 25}[/tex]

[tex]d = \sqrt{2} \times \sqrt{25}[/tex]

[tex]d = 5\sqrt{2}[/tex]

So the correct answer is:

c) 5√2 cm

What is the image of R for a dilation with center (0,0) and a scale factor of 1 1/2?

Answers

Answer: The image is (6,-3)

Step-by-step explanation:

The coordinates of R is  ( 4,-2)  and to find the image using the scale factor 1.5 you will multiply the x coordinates by 1.5 and the y coordinate also by 1.5 to have the new image of R.

4 * 1.5 = 6

-2 * 1.5 = -3

The new coordinates care (6, -3)

A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)(9,11). If this current flows through a 2-ohm resistor, find the probability density function of the power P = 2I^2P=2I 2 .

Answers

Answer:

Step-by-step explanation:

A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)

[tex]p_1=\{^{\frac{1}{2}:9\leq i\leq 11}_{0:otherwise[/tex]

Now define

[tex]p = 2I^2[/tex]

[tex]\Rightarrow I^2=(\frac{p}{2} )\\\\\Rightarrow I=(\frac{p}{2} )^{\frac{1}{2} }\\\\\Rightarrow h^{-1}(p)=(\frac{p}{2} )^{\frac{1}{2}}[/tex]

[tex]\frac{dh^{-1}}{dp} =\frac{d[h^{-1}(p)]}{dp} \\\\=\frac{d(p/2)^{\frac{1}{2} }}{dp}[/tex]

[tex]=\frac{1}{2} \times \frac{1}{2} (\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{4}(\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{2}(\frac{2}{p} )^{{\frac{1}{2}} }[/tex]

using the transformation method, we get

[tex]f_p(p)=f_1(h^{-1}(p))|\frac{d[h^{-1}(p)]}{dp} |\\\\=\frac{1}{2} \times \frac{1}{4} (\frac{2}{p} )^{\frac{1}{2} }\\\\=\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} }[/tex]

[tex]f_p(p)=\{^{\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} },162\leqp\leq 242} }_{0,otherwise}[/tex]

4. Dean Pelton wants to perform calculations to impress the accreditation consultants, but upon asking for information about GPAs at Greendale Community College, Chang only tells Pelton that the GPAs are distributed with a probability density function f(x) = D(2 + e −x ), 2 ≤ x ≤ 4 where D was some unknown "Duncan" constant. How many student records have to be retrieved so that the probability that the average GPA is less than 2.3 is less than 4 percent?

Answers

Answer:

the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Step-by-step explanation:

Let assume that n should represent the number of the students

SO, [tex]\bar x[/tex] can now be the sample mean of number of students  in GPA's

To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]

⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]

However ;

[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]

[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]

Similarly;

[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]

⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]

⇒ [tex]D*4.117 = 1[/tex]

⇒ [tex]D= \dfrac{1}{4.117}[/tex]

[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]

∴  [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]

Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]

Using Chebysher one sided inequality ; we have:

[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]

So; [tex](\omega = \bar x - \mu)[/tex]

⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]

∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]

To determine n; such that ;

[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]

⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]

[tex]n \geq 16.83125[/tex]

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

The sum of one and the product of 4 and a number x

Answers

Answer:

1 + 4x

Step-by-step explanation:

Let's break this down.

"The sum of one" means that something is being added to the number one:

1 +

"and" whatever comes after the word 'and' will be added to the number one

"the product of 4 and a number x" this means that the number four and the variable x are being multiplied:

4x

Put it together:

1 + 4x

Therefore, the expression is 1 + 4x.

if a-2= (2^2/3+2^1/3) find a^3-6a^2+12a-14​

Answers

Answer:

Step-by-step explanation:

7. 1, for r = 0 - 1, for r = 1 Hence, determine alo. Using characteristic root ... find the solution of the recurrence relation y, + 9 y, 2 = 6y, 1, subjected to the ... Solve a, -5a, 1 + 6a, 2 = 0 , given initial conditions ao = 2 and a1 = 5. ... Solve the recurrence relation a, – 7a, 1 + 16a, 2 – 12a, 3 = 0 for n > 3 with ... 2"; 3. a = (2)” – n.

Answer:

2

Step-by-step explanation:

I solved in the picture

Hope this helps ^-^

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures wide. The biologist estimates she will need of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to significant digits.

Answers

The complete question is;

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres

Answer:

10.5 atm

Step-by-step explanation:

Formula for Volume of a sphere is;

V = (4/3)πr³

r = 78/2 = 39 cm

V = (4/3)π(39)³

V = (4/3)*π*59319

V = 248475 cm³

Now, from conversions, 1000 cm³ = 1L

So,

V = 248475/1000

V = 248.5 L

This is the volume of the storage tank

If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:

From Boyles law,

P1 × V1 = P2 × V2

Thus;

(1 atm) × (2600 L) = (P2) × (248.5 L)

P2 = 2600/248.5

P2 = 10.463 atmospheres

Approximating to 3 significant figures is; P2 = 10.5 atm

Find the circumference of each circle, use 3.14 for . Include units and round to the nearest tenth. Show work





7. The circumference of a circle is 34.54 cm. What is the diameter and radius of the circle? (Show work)




8. What is the circumference of a circle in terms of , if it has a radius of 3.5 in?
(in terms of means do not substitute 3.14 for pi, leave the symbol in the final answer)

Answers

Answer:

Answer:-

a) The circumference of the circle  C = 21.98 m

b) The circumference of the circle  C = 37.68 ft

c)  The circumference of the circle  C = 40.82 km

d) The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

e) The circumference of the circle = 21.98 inches

  Step-by-step explanation:

a)  In First diagram

Given radius of the circle 'r' = 7.1 m

  The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (7.1)

                                                            C = 21.98 m

The circumference of the circle  C = 21.98 m

b) In second diagram

Given diameter of the circle 'd' = 12 ft

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×12

The circumference of the circle  C = 37.68 ft

c)

Given diameter of the circle 'd' = 13 km

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×13

 The circumference of the circle  C = 40.82 km

   

7) The circumference of the circle  C = 2πr

    Given The circumference of a circle is 34.54 cm

          Now       2πr = 34.54

                   2(3.14) r = 34.54

                           [tex]r = \frac{34.54}{3.14} = 11[/tex]

   The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

8) Given radius of the circle 'r' = 3.5 inches

   The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (3.5)

                                                            C = 21.98

  The circumference of the circle = 21.98 inches

 

find ∠AEC in the figure below.

Answers

Answer:

  C. 105°

Step-by-step explanation:

Angles BED and CED are supplementary, so ...

  (2y +x) +(-2y +3x) = 180

  4x = 180

  2x = 90

Substituting this into the expression for angle AEB, we have ...

  Angle AEB = (90 -15)° = 75°

Angle AEC is the supplement to that, so is ...

  ∠AEC = 180° -75° = 105° . . . . . matches choice C

Answer: C. 105

Step-by-step explanation:

Adding BED and DEC for being adjacent angles we obtain:

[tex]2y+x +-2y+3x = 180\\4x = 180\\x=45\\[/tex]

Substituting x in BEA

[tex]BEA=2(45)-15=75[/tex]

Adding BEA and AEC for being adjacent angles we obtain:

[tex]BEA+AEC=180\\AEC=180-BEA\\AEC=180-75\\AEC=105[/tex]

Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, what is the probability that none of them voted in the last election

Answers

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that [tex]p = 0.42[/tex]

Three Americans are randomly selected

This means that [tex]n = 3[/tex]

What is the probability that none of them voted in the last election

This is P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]

19.51% probability that none of them voted in the last election

1. The mean of the data set{9,5,y,2,x} is twice the data set {8,x,4,1,3}. What is (y-x) squared.
2. How many alcohol must be added to480 grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?

Answers

Answer:

1. (y - x)²  = 256

2. 128g needed to be added

Step-by-step explanation:

1.

9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)

16 + y + x = 32 + 2x

y - x = 16

∴ (y - x)²  = 256

2.

x = mass of alcohol to add

480 × 0.24 = 115.2 ← current mass of alcohol

0.4(480 + x) = 115.2 + x      (×5)

2(480 + x) = 576 + 5x

960 + 2x = 576 + 5x

3x = 384

x = 128g

Which statements are true?
If all angles of a quadrilateral are right angles, then the quadrilateral must be a square.
Two shapes are similar if and only if their corresponding angles are equal.
All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º.
if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
There are three vertices in a triangle, or there are four sides in a pentagon.
Any two triangles are either similar or congruent.

Answers

Answer:

Step-by-step explanation:

1) If all angles of a quadrilateral are right angles, then the quadrilateral must be a square. This is not true because the quadrilateral can also be a rectangle.

2) Two shapes are similar if and only if their corresponding angles are equal. This is true.

3) All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º. This is false because the sum of the angles is 360°

4) if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus. This is true.

5) There are three vertices in a triangle, or there are four sides in a pentagon. This is false because a Pentagon has 5 sides.

6) Any two triangles are either similar or congruent. This is not true. Congruent triangles are always similar

Therefore, the true statements are 2 and 4

Answer:

its B and D

Step-by-step explanation:





Mai deposited $4000 into an account with 4.8% interest, compounded quarterly. Assuming that no withdrawals are made, how much will she have in the
account after 7 years?
Do not round any intermediate computations, and round your answer to the nearest cent.

Answers

Answer:

5,586.17

Step-by-step explanation:

A = $ 5,586.17

A = P + I where

P (principal) = $ 4,000.00

I (interest) = $ 1,586.17

Compound Interest Equation

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

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Is​ f(x) continuous at x equals 4​? Why or why​ not? A. ​No, f(x) is not continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. ​Yes, f(x) is continuous at x equals 4 because f (4 )exists. C. ​No, f(x) is not continuous at x equals 4 because f (4 )is undefined. D. ​Yes, f(x) is continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )equals f (4 ).

Answers

Corrected Question

Is the function given by:

[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex] ​

continuous at x=4​? Why or why​ not? Choose the correct answer below.

Answer:

(D) ​Yes, f(x) is continuous at x = 4 because [tex]Lim_{x \to 4}f(x)=f(4)[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]

A function to be continuous  at some value c in its domain if the following condition holds:

f(c) exists and is defined.[tex]Lim_{x \to c}$ f(x)[/tex] exists. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]

At x=4

[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]

Therefore: [tex]Lim_{x \to 4}f(x)=f(4)=2[/tex]

By the above, the function satisfies the condition for continuity.

The correct option is D.

Use the area to find the radius. If you could include steps that’ll be very helpful :)

Answers

Answer:

Radius = 13 m

Step-by-step explanation:

Formula for area of circle is given as:

[tex]A = \pi {r}^{2} \\ \\ \therefore \: 169\pi \: = \pi {r}^{2} \\ \\ \therefore \: {r}^{2} = \frac{169\pi }{\pi} \\ \\ \therefore \: {r}^{2} = 169 \\ \\ \therefore \: {r} = \pm \sqrt{169} \\ \\\therefore \: r = \pm \: 13 \: m \\ \\ \because \: radius \: of \: a \: circle \: can \: not \: be \: a \: negative \: \\quantity \\ \\ \huge \red{ \boxed{\therefore \: r = 13 \: m }}[/tex]

The length and with of a rectangle are consecutive odd integers . The perimeter is 104 meters .find the length and with

Answers

Answer:

  25 m, 27 m

Step-by-step explanation:

The perimeter is twice the sum of length and width, so that sum is 52 m. Half that is the average of length and width, so will be the even integer between the two consecutive odd integers.

  52/2 = 26

The length and width are 25 m and 27 m.

a triangle has an area of 15 cm. a similar triangle is drawn using a scale factor of 3.5. what is the area of the similar triangle to the nearest square cm?​

Answers

Answer:

  184 square cm

Step-by-step explanation:

The ratio of areas is the square of the ratio of the scale factor. The larger triangle has an area of ...

  (15 cm²)(3.5²) = 183.75 cm²

The area of the similar triangle is about 184 cm².


A farmer knows that every 50 eggs his chickens lay, only 45 will be marketable. If his
chickens lay 1000 eggs in a week, how many of them will be marketable?

Answers

Answer:

900 eggs

Step-by-step explanation:

45/50 are marketable

divide the top and bottom by 5

9/10

Multiply this fraction by the 1000 eggs laid

9/10 *1000

900 eggs will be marketable

Answer:

900

Step-by-step explanation:

A.13.4 feet
B.13.1 feet
C.18 feet
D.10.4 feet

Answers

Answer:

13.4 feet

Step-by-step explanation:

use physagorean law

√12²+6²=cable

=13.4 feet

Determine the magnitude of the resultant force by adding the rectangular components of the three forces.
a) R = 29.7 N
b) R = 54.2 N
c) R = 90.8 N
d) R = 24.0 N

Answers

C the answer is C CCCCCCCC

You are writing music for a movie and you have to synchronize the music to the amount of frames per click in it. It's a battle scene so you want fast, energetic and exciting music. You choose a Presto tempo marking of 200 beats per minute. How many picture frames are there per each tempo click? (Round to the nearest whole number and write only the number.)

Answers

Answer: 7.2 frames per bit.

Step-by-step explanation:

Our teempo is 200 bpm.

in one minute we have 60 seconds, so here we have:

200b/60s = 3.33 bits per second.

For movies, the standar is 24 frames per second

now, we can take the quotient between the frames per second and the bits per second and get the frames per bit.

24fps/3.33bps = 7.2 frames per bit.

What is the approximate value of sin B?
B
>
17.46
7
A
16

Answers

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

AB = 7 units

BC = 17.46 units

AC = 16 units

Now we apply the sine rule in the given triangle ABC,

SinB = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

        = [tex]\frac{AC}{BC}[/tex]

        = [tex]\frac{16}{17.46}[/tex]

        = 0.916

        ≈ 0.92

Therefore, Option (B) will be the answer.

Answer:

DIFFERENT PICS

Step-by-step explanation:

I had one and the awnser was 0.40, and C had a arch whereas B did not.

Other Questions
The sum of the interior angles of a regular polygon is 1800 degrees. How many sides does is have? *1 point9 sides10 sides11 sides12 sides My brother ________________ to dance but he loves having a good talk. (not like) Consider an experiment where you digest a DNA molecule with restriction enzyme BclI. You resolve the products of the digest by gel electrophoresis. Then, you cut out each of the resulting two bands from the gel and sequence the DNA. The sequencing results return two DNA segments.Segment 15 CCGCGGT 33 GGCGCCACTAG 5Segment 25 GATCAGGATCC 33 TCCTAGG 51. What is the sequence of the BclI recognition site?2. What type of ends do the products have? Which is the balanced equation for S3 + O2 SO2?O O O OS8 + 016 8S02Se + O S + O2Se + O S0Sg + 802 8802 Suppose that the functions u and w are defined as follows. Why didnt Florida become a state as soon as it had written a constitution To increase productivity, your project team has completed the task to develop potential ideas for approval by senior management. While receiving feedback and guidance (message-receiving process) from senior management, you should IDEALLY: Killing pathogens and then using them to provide the body with active immunity is called ______. This is often done in young children.When the immune system treats otherwise harmless substances, such as pollen, as if they were invaders, a/n ______ can occur.HIV is a virus that attacks ______ in the body, weakening the immune system.Polio used to be fairly common and devastating. Thanks to widespread vaccination against polio, the disease is now considered _______, no longer infecting nearly as many people as it once did.Arthritis is an example of a/n _______, where part of a persons body is identified as foreign and attacked by the persons immune system.Respond to the following based on your reading.Colonization is largely blamed for bringing smallpox to the Americas. Why was this disease so devastating to Native Americans? Why can we now travel to different parts of the world and avoid contracting analogous diseases? 11. In a group of six young pupils the mean weekly amount of pocket money is 5. When a new pupil joins, the mean weekly pocket money increases to 6. What does the new pupil receive each week ? B is known in the trade as a trader and merchant of soybeans. A entrusts a load of soybeans to B for storage in B's warehouse. Secretly, B delivers the goods to an ocean carrier in return for a bill of lading. B then sells the document covering a shipment of soybeans to C, who has purchased soybeans from B in the past. C pays for the document through its bank. B absconds with the money. In this case:________.A) B is guilty of a crime under the Uniform Commercial Code.B) C is probably not a good faith purchaser.C) C takes paramount title.D) B and the carrier are liable for a conspiracy to commit fraud. g The transactions of Spade Company appear below. Kacy Spade, owner, invested $100,750 cash in the company in exchange for common stock. The company purchased office supplies for $1,250 cash. The company purchased $10,050 of office equipment on credit. The company received $15,500 cash as fees for services provided to a customer. The company paid $10,050 cash to settle the payable for the office equipment purchased in transaction c. The company billed a customer $2,700 as fees for services provided. The company paid $1,225 cash for the monthly rent. The company collected $1,125 cash as partial payment for the account receivable created in transaction f. The company paid a $10,000 cash dividend to the owner (sole shareholder). Required: 1. Prepare general journal entries to record the transactions above for Spade Company by using the following accounts: Cash; Accounts Receivable; Office Supplies; Office Equipment; Accounts Payable; Common Stock; Dividends; Fees Earned; and Rent Expense. 2. Post the above journal entries to T-accounts, which serve as the general ledger for this assignment. Miquel babysits for 3 hours and eams $15. Which represents the unit rate?0 $1 per 5 hoursO $15 per hour0 1 hour per $5o 55 per hour What determines the average kinetic energy of the particles in a gas?A.the number of collisionsB.the number of particlesOC.the size of the particlesD.the temperature What is the ratio of quadrilaterals to shapes?Write the ratio as a fraction using the / symbol. In the movie, Tim says that chlorophyll traps photons. What are photons? Simplify the expression (3 - 4i)(1 + 5i) - (2 - i). Show your work Bonita said that the product of 5/6 x 1 2/3 is 7/3.How can you tell that her answer is wrong. The table represents a linear function.What is the slope of the function?0-6O -40 4O 6 When vinylcyclohexane is treated with in dichloromethane, the major product is (2-bromo ethylidene)cyclohexane . Account for the formation of this product by drawing the structure of the most stable radical intermediate. Include all valence lone pairs in your answer. Include all valence radical electrons in your answer. Work out the value of 2^3 + 5^2