(4CQ) Determine whether the series 3/2+9/8+27/32+...is convergent or divergent.

Answer:

(3250/100)*80 = $ 2600 - 3250 = $650

Step-by-step explanation:

Answer:

a. Ratio of girls to all students 5:11

b. Ratio of girls to all students n:m+n

c. Ratio of girls to boys 5:6

Step-by-step explanation:

In order to find each of these, we simply need to look at these as a comparison of two data points.

a. In this example, we are looking for girls to all students. We already who there would be 5 girls in the comparison. Then we need to find the whole amount, which is girls + boys (6 + 5 = 11)

5:11

b. In this example, we are looking for girls to all students. We already who there would be n girls in the comparison. Then we need to find the whole amount, which is girls + boys (m + n)

n:m+n

c. In this example, we are looking for girls to boys. We already who there would be 5 girls in the comparison. Then we need to find the boys amount, which is whole - girls (11 - 5 = 6)

5:6

Final answer:

The ratio of girls to all students in a class with a boy-girl ratio of 6 to 5 is 5 to 11. The general ratio of girls to all students with a boy-girl ratio expressed as m:n is n:(m+n). Lastly, if five elevenths of the class are girls, then the ratio of girls to boys is 5 to 6.

Explanation:

Understanding Ratios in a Classroom Setting

The ratio of boys to girls in a class is initially given as 6 to 5. To find the ratio of girls to all the students in the class, the sum of the parts of the ratio must first be calculated, which is 6 (boys) + 5 (girls) = 11 (total students).

Therefore, the ratio of girls to the total number of students is 5 to 11. This is because for every 11 students, 5 are girls. If the ratio of boys to girls is expressed as m:n, then the ratio of girls to all students will be n:(m + n).

For a scenario where five elevenths of the class are girls, the ratio of girls to boys needs to be determined. As five elevenths represent the girls, six elevenths must represent the boys, since they sum up to the whole, which is one (or 11/11). Therefore, the ratio of girls to boys is 5:6.

Answer:

$13.68

Step-by-step explanation:

3.42 x 4

Final answer:

To find the total cost of 4 baseballs, each costing $3.42, we multiply the cost of one baseball by the number of baseballs, resulting in a total cost of $13.68.

Explanation:

The question asks to calculate the total cost of 4 baseballs, provided that each costs $3.42. To find the total cost, we need to multiply the cost of one baseball by the number of baseballs that were purchased. Hence, the calculation of the total cost of baseball is given by $3.42 (cost of one baseball) × 4 (number of baseballs) = $13.68. Therefore, the total cost of the 4 baseballs is $13.68.

if it is asking for compound interest your answer should be 49761.9

Answer:

  Triangles BPA and DPC are congruent.

Step-by-step explanation:

The statement above is the only one of the bunch that is true, so is the best selection.

You don't even need to worry too much about how you might make the proof. You just need to be concerned with which are plausible answers. There's only one.

Answer:

B. (0,6)

Step-by-step explanation:

To solve this question, you'll need to figure out what the final point is after reflecting each point. A quick way to figure this out is by multiplying (-1) to the x-coordinate.

When you reflect A. (2,0) over the y-axis, the point becomes (-2,0).

When you reflect C. (3,3) over the y-axis, the point becomes (-3,3).

When you reflect D. (5,5) over the y-axis, the point becomes (-5,5).

The only answer that does not change location is B. (0,6) as it stays at (0,6). If you multiply 0 by any number, it will always stay 0.

Multiplying the x-coordinate by (-1) to find the reflection point only works if you are reflecting it over the y-axis. You would multiple the y-coordinate by (-1) if you were reflecting over the x-axis.

Answer:

Part a) [tex]m<HIG=40\°[/tex]

Part b) IHG is a semicircle and GJI is a semicircle

Part c) HIJ is a major arc and HIJG is a major arc

Part d) [tex]arc\ GH=80\°[/tex]

Part e) [tex]arc\ GJI=180\°[/tex]

Step-by-step explanation:

Part a) Give an inscribed angle

we know that

The inscribed angle measures half that of the arc comprising

so

in this problem m<HIG is an inscribed angle

[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]

[tex]arc\ HG=80\°[/tex] ----> by central angle

substitute

[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]

Part b) Give a semicircle

we know that

The diameter divide the circle into two semicircles

so

GI is a diameter

therefore

IHG is a semicircle

GJI is a semicircle

Part c) Give a major arc

we know that

The measure of a major arc is greater than 180 degrees

therefore

HIJ is a major arc

HIJG is a major arc

Part d) Measure of arc GH

we know that

[tex]arc\ GH=m<HFG[/tex] ----> by central angle

so

[tex]arc\ GH=80\°[/tex]

Part e) Measure of arc GJI

we know that

[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle

Answer:

[tex]\large\boxed{-6y^2+12y+4}[/tex]

Step-by-step explanation:

[tex](2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4[/tex]

Answer:

YES

YES

NO

YES

Step-by-step explanation:

Assuming that the value is [tex]\dfrac{4}{9}[/tex].

Let's take each of the equations and check if the fraction makes the equation true.

When multiplying a whole number to a fraction, it is the same as multiplying the whole number to the numerator and dividing the total by the denominator.

[tex]63*\dfrac{4}{9}=28[/tex]

[tex]\dfrac{63*4}{9}=28[/tex]

[tex]\dfrac{252}{9}=28[/tex]

[tex]28=28[/tex]    YES

[tex]18*\dfrac{4}{9}=8[/tex]

[tex]\dfrac{18*4}{9}=8[/tex]

[tex]\dfrac{72}{9}=8[/tex]

[tex]8=8[/tex]    YES

[tex]96*\dfrac{4}{9}=42[/tex]

[tex]\dfrac{96*4}{9}=42[/tex]

[tex]\dfrac{384}{9}=42[/tex]

[tex]42.67=42[/tex]    NO

[tex]36*\dfrac{4}{9}=16[/tex]

[tex]\dfrac{36*4}{9}=16[/tex]

[tex]\dfrac{144}{9}=16[/tex]

[tex]16=16[/tex]    YES

Answer:

yes

yes

no

yes

hope this helps!!

Answer:

  y = tan(x -π) -1

Step-by-step explanation:

It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...

  tan(x -π) = tan(x)

so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.

The appearance of the graph is of ...

  y = tan(x) -1

The choice that is equivalent to this is ...

  y = tan(x -π) -1

Answer:

y = tan (x-pi)-1

Step-by-step explanation:

The function in the graph is a periodic function with intervals of pi and having discontinuities at regular intervals.

Hence this must be a transformation of the original trignometric funciton

tan x.   y intercept is at -1 which shows that there is a vertical shift of 1 unit down.

Hence the funciton is y = tanx-1

But tan x is not given in any of the options.

Let us check which is equivalent to tan x-1

We find that tan(x-pi) = -tan (pi-x) = -(-tanx) = tanx

Hence the option 3 is the right answer

Answer:

  C)  78 ft

Step-by-step explanation:

The side opposite the angle has the ratio to the hypotenuse:

  Sin = Opposite/Hypotenuse

Then the solution to this problem is found by substituting the given information and solving for the height.

  sin(45°) = height/(110 ft)

  (110 ft)·sin(45°) = height ≈ 77.7817 ft

Rounded to the nearest foot, the crane can raise material to a height of 78 ft.

Answer:

  90°

Step-by-step explanation:

Supplementary means they add to 180°. Vertical angles are congruent, so they must both be 180°/2 = 90°.

Answer:

90

Step-by-step explanation:

Did the Geometry quiz 2021

Plz click the Thanks button!

<Jayla>

Answer:

see explanation

Step-by-step explanation:

Isolate r² by dividing both sides by πh

r² = [tex]\frac{V}{h\pi }[/tex]

Take the square root of both sides

r = ± [tex]\sqrt{\frac{V}{h\pi } }[/tex]

The negative part can be  discarded as r > 0, hence

r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]

the answer is 942.because the formula is V=Bh. V=pir2h. so V= 3.14×5squared×12. so 3.14×25×12. 25×12=300. and 3.14×300=942

Answer:

Translated to the left 5 units and up 5 units and compressed horizontally by 2 units.

Step-by-step explanation:

The  parent function given is [tex]f(x)=x^2[/tex]

This function has its vertex at the origin.

If we move this function 5 units  to the left and 5 units up, then its vertex will now be at [tex](-5,5)[/tex].

If the parent function is then compressed horizontal by a factor of 2, then the transformed function will now have equation.

[tex]g(x)=2(x+5)^2+5[/tex]

1/2÷1/6

=

1/2*6/1

=

6/2

=

3

Answer:

Quotient would be 3.

Step-by-step explanation:

The model below can be used to find the quotient of one over two dividend by one over six.

We will rewrite the problem :

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{6}[/tex]

As we know when we divide the two fractions, we must invert the second fraction and put the sign of multiplication in place of division sign and multiply.

So now we can write the problem as :

[tex]\frac{1}{2}[/tex] × [tex]\frac{6}{1}[/tex]

= [tex]\frac{6}{2}[/tex]

= 3

Quotient would be 3.

Answer:

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

The other root of the quadratic equation is -2, and the coefficient c is -106, found using the sum and product of roots formulas.

The other root and the coefficient c of the quadratic equation 10x²- 33x + c = 0, given that one of the roots is 5.3. Using the fact that the sum of the roots of a quadratic equation ax² + bx + c = 0 is equal to -b/a, we can find the other root. With one root known to be 5.3 and a = 10, b = -33, the sum of the roots must be 3.3. Therefore, the other root is 3.3 - 5.3 = -2. To find the coefficient c, we use the fact that the product of the roots of a quadratic equation is equal to c/a. Thus, c = 5.3 * (-2) * 10 = -106. The other root of the equation is -2, and the coefficient c is -106.

Answer:

$75000

Step-by-step explanation:

5% of $60000 is $3000 and $3000 x 5 is $15000 and $15000 + $60000 is $75000

To calculate the total salary over 5 years with an initial salary of $60,000 and a 5% annual raise, you add the salary of each year considering the raise. The salaries over 5 years will be $60,000; $63,000; $66,150; $69,457.50; $72,930.38 respectively, amounting to a total of $331,537.88, which is approximately $331,538.

The question asks how much money you would earn total after 5 years of working at a company starting with a $60,000 salary and receiving a 5% raise each year. This is a problem of geometric progression in mathematics. To calculate the total amount earned over 5 years, we have to apply the formula for the sum of a geometric series because the salary increases by a fixed percentage each year. The salary each year is as follows: Year 1 - $60,000, Year 2 - $60,000*1.05, Year 3 - $60,000*(1.05)^2, Year 4 - $60,000*(1.05)^3, and Year 5 - $60,000*(1.05)^4.

Here is the calculation step-by-step:

Now, add up the salaries for each year to find the total earnings:

Add up these amounts to get the total earnings after 5 years:

Total = $60,000 + $63,000 + $66,150 + $69,457.50 + $72,930.38 = $331,537.88, which can be rounded to approximately $331,538.

Therefore, the correct answer is: $331,538.

Answer:D) 144

Step-by-step explanation:12*12=144

Answer:

the answer is 144

Step-by-step explanation:

Answer:

6x-5y=-10

Step-by-step explanation:

We are given an equation in words and we are to translate it and then re-write its standard form:

'y space equals space 6 over 5 x space plus space 2 '

[tex] y = \frac { 6 } { 5 } x + 2 [/tex]

Re-arranging this given equation to get:

[tex] y - 2 = \frac { 6 } { 5 } x [/tex]

[tex]5(y-2)=6x[/tex]

[tex]5y-10=6x[/tex]

[tex]6x-5y=-10[/tex]

So the correct answer option is 6x-5y=-10.

Answer:

No solution.

Step-by-step explanation:

The given functions are

[tex]y=\cos2x[/tex] and [tex]y=1-\sin^2x[/tex].

To find the point of intersections of the graphs of the two functions: we equate them and solve for [tex]x[/tex].

[tex]\cos2x=1-\sin^2x[/tex]

Recall the double angle identity; [tex]\cos2x=cos^2x-sin^2x[/tex]

Apply this identity to obtain;

[tex]cos^2x-sin^2x=1-\sin^2x[/tex]

[tex]\Rightarrow cos^2x=1[/tex]

[tex]\cos x=\pm1[/tex]

[tex]x=0\:or\:x=\pi[/tex]

if the interval is [tex]0\le x\le \pi[/tex], then the two graphs intersect at [tex]x=0\:or\:x=\pi[/tex]

But [tex]x=0\:and\:x=\pi[/tex] does not belong to the open interval [tex]0\:<\:x\:<\:\pi[/tex]

No point of intersection.

Answer:

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}[/tex]

We have:

[tex]DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788[/tex]

Substitute:

[tex]\dfrac{75}{0.9659}=\dfrac{EF}{0.788}[/tex]          cross multiply

[tex]0.9659EF=(75)(0.788)[/tex]

[tex]0.9659EF=59.1[/tex]          divide both sides by 0.9659

[tex]EF\approx61.19[/tex]

The length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have:

DE = 75 inches

By using the sin law:

sin52/EF = sin75/DE

sin52/EF = sin75/75

sin52/EF = 0.0128

EF = 61.185 ≈ 61.19 inches

Thus, the length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

ANSWER

[tex]y = - 5[/tex]

EXPLANATION

The horizontal asymptote of a general exponential function,

[tex]f(x) = a {(b)}^{x} + c[/tex]

is y=c.

The given exponential function is

[tex]f(x) = 4{(2)}^{x} - 5[/tex]

By comparing the given function to

[tex]f(x) = a {(b)}^{x} + c[/tex]

we have c=-5, therefore the horizontal asymptote is

[tex]y = - 5[/tex]

Answer:

B. x = 4

Step-by-step explanation:

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

[tex]\log_bm+\log_bn=\log_bmn[/tex]

Using this law, we can combine and rewrite our initial equation as

[tex]\log_2(x\cdot(x-2))=3\\\log_2(x^2-2x)=3[/tex]

Remember that logarithms are simply another way of writing exponents. The logarithm [tex]\log_28=3[/tex] is just another way of writing the fact [tex]2^3=8[/tex]. Keeping that in mind, we can express our logarithm in terms of exponents as

[tex]\log_2(x^2-2x)=3\rightarrow2^3=x^2-2x[/tex]

2³ = 8, so we can replace the left side of our equation with 8 to get

[tex]8 = x^2-2x[/tex]

Moving the 8 to the other side:

[tex]0=x^2-2x-8[/tex]

We can now factor the expression on the right to find solutions for x:

[tex]0=(x-4)(x+2)\\x=4, -2[/tex]

The only option which agrees with our solution is B.

Answer:

The answer is:

        [tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]

Step-by-step explanation:

We are given a logarithmic expression as:

[tex]\log_2 x+log_2 (x-2)=3[/tex]

As we know that:

[tex]\log_a x=\dfrac{\log x}{\log a}[/tex]

Hence, we get the logarithmic expression as follows:

[tex]\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}=3[/tex]

We know that we can get the system of equations as follows:

[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}[/tex]

and

[tex]y_2=3[/tex]

Hence, when we plot the graph for this system of equations we see that the point of intersection of the graph is: (4,3)

Hence, the solution is the x-value of the point of intersection of the two equations.

Hence, x=4 is the solution.

Hence, the correct option is:

  [tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]

simplify :7x + 3x - 5 + 8x + 5 = 180

x = 10

Answer:

$455.97

Step-by-step explanation:

119000 × 0.12 = 14280

119000 - 14280 = 104720

104720 × 1.045 = 109432.4

109432.4/(20×12)

109432.4/240

455.97 a month

Answer:

$662.46

Step-by-step explanation:

Answer:

  a straight line: y = x -5, with a hole at (4, -1)

Step-by-step explanation:

The rational function can be simplified to ...

  [tex]f(x)=\dfrac{x^2-9x+20}{x-4}=\dfrac{(x-5)(x-4)}{(x-4)}\\\\f(x)=x-5\qquad\text{$x\ne 4$}[/tex]

The graph of this is a straight line, with a hole at x=4, where the function is not defined.