find the sum of the geometric series. 14-7+(7/2)-(7/4)+

Answer:

Snakes have 35000 cm³ space in their habitat.

Step-by-step explanation:

First Terrarium has the dimensions of (length×width×height) =(40×25×20)=Volume of Terrarium(V1)

V1 = 20000 cm³

Similarly volume V2 of the second terrarium = (25×30×20) cm³

V2=15000 cm³

Therefore total space for the snakes V1+V2 =20000+15000 cm³

                                                                         =35000 cm³

For two events A and B,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

We're given all of the probabilities on the right hand side:

[tex]P(\text{cook OR sew})=P(\text{cook})+P(\text{sew})-P(\text{cook AND sew})[/tex]

[tex]\implies P(\text{cook OR sew})=42\%+23\%-7\%=58\%[/tex]

The keyword here is "or", this means it wants the probability of finding a person who likes to cook -- or a person who likes to sew.

We are given both of these probabilities, and to find the probability of finding someone who likes to do activity A OR activity B, we simply add the probability of activity A and activity B.

42 + 23 = 65% of members like to cook or like to sew.

Answer:

118

Step-by-step explanation:

simple:

59.50 - 30.00=29.50

29.50 divided by 0.25= 118

in equation form

y=mx+b

59.50=0.25(x)+30.00

so the output (y) is the total money owed (59.50) and the 0.25 cents is the slope or unit rate and the 30.00 in this context is the monthly fee. So to find x= number of texts sent, you have to firstly get rid of the monthly fee, you subtract 30.00 by itself so it cancels out and you gotta do the same to the other side (the output), ( 59.50 - 30.00)= 29.50 and after that you have the remaining of 29.50=0.25x , now you have to divide 0.25 to both sides so 0.25/0.25=1 and basically 1x=x , now you divide 29.50/0.25=118    now you solved for x! The amount of texts sent=118

Answer: B

Step-by-step explanation:

[tex]P=100e^{(.70)t}[/tex]

[tex]300=100e^{.7t}[/tex]

[tex]3=e^{.7t}[/tex]

[tex]ln3=lne^{.7t}[/tex]

[tex]ln3=.7t[/tex]

[tex]\dfrac{ln3}{.7}=t[/tex]

1.6 = t

Answer:

Option B. 1.6 Hours

Step-by-step explanation:

The model for the population of bacteria is growing by :

[tex]P=100e^{(0.70)t}[/tex]

Where P = Number of colonies

and t = time in hours.

So, now put  the value of  P = 300 in the given model and obtain the value of t.

⇒ [tex]300=100e^{(0.70)t}[/tex]

⇒ [tex]3=e^{(0.7)t}[/tex]

Taking the natural log in on both the side

⇒ [tex]In3=Ine^{(0.7)t}[/tex]

⇒ [tex]In3=0.7t[/tex]

⇒ [tex]t=\frac{In3}{0.7}[/tex]

⇒ t = 1.6 hours

Therefore, The correct option is B). 1.6 hours

The formula for the perimeter of a rectangle is P = 2L + 2W

you are given P (perimeter) and l (length.

Replace the letters withe the given information and solve for width:

76 = 2(31) +2W

Simplify:

76 = 62 + 2w

Subtract 62 from both sides:

14 = 2w

Divide both sides by 2:

W = 14/2

W = 7 cm

The width is 7 cm.

i think it will be 5 minutes

Answer:

D is the answer

Answer:

The correct option is 4. The lengths of side SR and side S'R' are in the ratio 1:3.

Step-by-step explanation:

The vertices of polygon are P(0,-3), Q(3,-2), R(3,1), S(0,2), T(-2,0).

The vertices of image are P'(0,-9), Q'(9,-6), R'(9,3), S'(0,6), T'(-6,0).

It is given that polygon P'Q'R'S'T' is the image of polygon PQRST after dilation with a scale factor of 3. It means both polygons are similar.

The corresponding angles of similar figure and same and the corresponding sides are proportional. It means the sides of image are three times of the corresponding sides of pre-image.

SR and S'R' are corresponding sides.

[tex]S'R'=3\times SR[/tex]

[tex]\frac{S'R'}{3}=SR[/tex]

[tex]\frac{1}{3}=\frac{SR}{S'R'}[/tex]

[tex]1:3=SR:S'R'[/tex]

The lengths of side SR and side S'R' are in the ratio 1:3.

Therefore the correct option is 4.

Answer:Han's mixture tastes stronger

Step-by-step explanation: Han's mixture tastes stronger, because...

Han's uses 6 2/3 cups of water for every 1 cup of orange juice concentrate.

Clare uses 71/2 cups of water for every 1 cup of orange juice concentrate.

Answer:

Han's juice has 15% concentration which is larger and hence, his juice will be stronger.

Step-by-step explanation:

It is required to find that which juice is stronger. So, we need to find the juice with maximum fraction or percentage of juice out of both the cases.

In first case, Clare mixes [tex]2\dfrac{1}{2}=\dfrac{5}{2}[/tex] cups of water with [tex]\dfrac {1}{3}[/tex] cup of orange juice. So, the concentration of the juice will be,

[tex]\dfrac{1/3}{5/2}=\dfrac{2}{15}=13.33\%[/tex]

In the second case, Han mixes [tex]1\dfrac{2}{3}[/tex]  cups of water with [tex]\dfrac{1}{4}[/tex] cup of orange juice.

So, the concentration of the juice will be,

[tex]\dfrac{1/4}{5/3}=\dfrac{3}{20}=15\%[/tex]

Therefore, out of the two cases, Han's juice has 15% concentration which is larger and hence, his juice will be stronger.

For more details, refer the link:

https://brainly.com/question/14780097?referrer=searchResults

Answer: The answer is (A) ΔCBA similar to ΔFED, (D) ΔBAC similar to ΔEDF and (E) ΔABC similar to ΔDEF.

Step-by-step explanation:  We are given a figure in which two similar triangles are shown. We are to select all the correct similarity statements that describes the relationship between the two triangles.

In ΔABC, we have

∠B is the right angle, AC is the hypotenuse and AB is the shortest side.

Similarly, ΔDEF, we have

∠E is the right angle, DF is the hypotenuse and DE is the shortest side.

Therefore, the corresponding pairs of vertices in the two triangles will be

(A and D), (B and E) and (C and F).

Hence, the correct similarity statements are

ΔCBA similar to ΔFED,

ΔBAC similar to ΔEDF

and

(E) ΔABC similar to ΔDEF.

Thus, (A), (D) and (E) are the correct options.

Q2 Answer: Experimental = 60%, difference = 10%

Step-by-step explanation:

The prime numbers between 1 and 8 are: 2, 3, 5, and 7.

Theoretical: [tex]\dfrac{4(prime)}{8(total)} = 50\%[/tex]

Experimental: [tex]\dfrac{12(prime)}{20(total)} = 60\%[/tex]

    Experimental - Theoretical

=       60%            -      50%

=                     10%

Problem 1

To find the sample mean, we simply add up all the 40 items and then divide by 40

I will add up the values row by row, and then add up the subtotals to get the grand total

row1: 39+31+38+40+29 = 177

row2: 32+33+39+35+32 = 171

row3: 32+27+30+31+27 = 147

row4: 30+29+34+36+25 = 154

row5: 30+32+38+35+40 = 175

row6: 29+32+31+26+26 = 144

row7: 32+26+30+40+32 = 160

row8: 39+37+25+29+34 = 164

Add up the subtotals: 177+171+147+154+175+144+160+164 = 1292

Divide this over 40: 1292/40 = 32.2

So the sample mean is therefore 32.2

-----------------------

To find the proportion of defective items, we count the number of times a value less than 26 shows up. That happens exactly two times. The first in row 4 (at the end of this row) is where a 25 shows up. Another copy of 25 shows up in row 8 (bottom row). There are no other values that are less than 26.

Divide this count (2) over the total sample size (40) and we get 2/40 = 1/20 = 0.05

-----------------------

In summary, 32.2 will go in the first box while 0.05 will go in the second box.

========================================

Problem 2

There are 4 values we want (2,3,5,7) out of 8 total (1,2,3,4,5,6,7,8) so 4/8 = 0.50 = 50% is the theoretical probability

This is the list of values given to us (I broke it up to help make the numbers more readable)

3, 4, 5, 2, 7

1, 3, 7, 2, 6

2, 1, 7, 3, 6

1, 8, 3, 5, 6

Of that list, the primes {3, 5, 2, 7, 3, 7, 2, 2, 7, 3, 3, 5} show up. There are 12 primes in this list out of 20. So the experimental probability is 12/20 = 3/5 = 0.60 = 60%

Therefore, the answer that goes in the "experimental probability" box is 60. The answer that goes in the second box is not 50%. I think your teacher is aiming for "10" to go in the second box because 60% is 10 percentage points higher than 50% (which was the theoretical probability found earlier)

-----------------------

In summary, 60 will go in the first box while 10 will go in the second box.

Answer:

If you multiply (12 x 48), you figure out how much she makes in a week ($576 a week). Then if there is 52 weeks in a year, subtract the number of weeks she gets off from 52, and multiply that number by 576 to get how much she is paid in a year. What I got from this, is that she has 1 week off. So my answer is she gets paid $29,376 a year. I hope this helps!

Answer:

Area of rectangle = 30 units

Step-by-step explanation:

vertices are (2,2),(-3,2),(2,8), and (-3,8)

Let find the distance between (2,2)  and (2,8). because they have same x values. that would be our width

distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}[/tex]

D = [tex]\sqrt{(2-2)^2 + (8-2)^2}=\sqrt(6^2) = 6[/tex]

Width = 6

Now we find distance between (2,2) and (-3,2) because they have same y values, that would be our length

distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_2)^2}[/tex]

D = [tex]\sqrt{(-3-2)^2 + (2-2)^2}=\sqrt(-5^2) = \sqrt(25)= 5[/tex]

length = 5

Area of rectangle = length * width = 5*6 = 30

Answer: 1/2 is the value b such that (b)^1 = 1/2, the fraction the isotope decays in one year.

Step-by-step explanation:

Answer:

0.609 / week  ( to nearest  thousandth)

or you can state it as 60.9% of a book per week

Step-by-step explanation:

That would be 14/23 =  0.609 / week

QUESTION 1  

If a function is continuous at [tex]x=a[/tex], then [tex]\lim_{x \to a}f(x)=f(a)[/tex]  

Let us find the limit first,  

[tex]\lim_{x \to 4} \frac{x-4}{x+5}[/tex]  

As [tex]x \rightarrow 4[/tex], [tex]x-4 \rightarrow 0[/tex],[tex]x+5 \rightarrow 9[/tex] and [tex]f(x) \rightarrow \frac{0}{9}=0[/tex]  

[tex]\therefore \lim_{x \to 4} \frac{x-4}{x+5}=0[/tex]  

Let us now find the functional value at [tex]x=4[/tex]  

[tex]f(4)=\frac{4-4}{4+5} =\frac{0}{9}=0[/tex]  

Since  

[tex]\lim_{x \to 4} f(x)=\frac{x-4}{x+5}=f(4)[/tex], the function is continuous at [tex]a=4[/tex].  

QUESTION 2  

The correct answer is table 2. See attachment.

In this table the values of x approaches zero from both sides.

This can help us determine if the one sided limits are approaching the same value.

As we are getting closer and closer to zero from both sides, the function is approaching 2.

The values are also very close to zero unlike those in table 4.

The correct answer is B

QUESTION 3

We want to evaluate;

[tex]\lim_{x \to 1} \frac{x^3+5x^2+3x-9}{x-1}[/tex]

using the properties of limits.

A direct evaluation gives [tex]\frac{1^3+5(1)^2+3(1)-9}{1-1}=\frac{0}{0}[/tex].

This indeterminate form suggests that, we simplify the function first.

We factor to obtain,

[tex]\lim_{x \to 1} \frac{(x-1)(x+3)^2}{x-1}[/tex]

We cancel common factors to get,

[tex]\lim_{x \to 1} (x+3)^2[/tex]

[tex]=(1+3)^2=16[/tex]

The correct answer is D

QUESTION 4

We can see from the table that as x approaches [tex]-2[/tex] from both sides, the function approaches [tex]-4[/tex]

Hence the limit is [tex]-4[/tex].

See attachment

The correct answer is option A

Answer:

Yes

Step-by-step explanation:

2√3 − 2√3 is equal to 0. So what we are trying to find out is if 0 is a rational number. 0 IS a ratinol number as it can be expressed as a fraction of integers.

Answer:

One number is [tex]\frac{5}{7}[/tex] and the other number is [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

Let x be the smaller number and y be the bigger number.

x = x

y = 5x

6x + 3y = 3

6x + (3 * 5x) = 3

6x + 15x = 3

(÷3)

2x + 5x = 1

7x = 1

x = [tex]\frac{1}{7}[/tex]

6x + 3y = 3

6([tex]\frac{1}{7}[/tex]) + 3y = 3

[tex]\frac{6}{7}[/tex] + 3y = 3

3y = 3 - [tex]\frac{6}{7}[/tex]

3y = [tex]\frac{15}{7}[/tex]

Divide both sides by 3 to get 1y:

y = [tex]\frac{5}{7}[/tex]

So one number is [tex]\frac{5}{7}[/tex] and the other number is [tex]\frac{1}{7}[/tex]

Answer:

Carol drank 0.5625 gallon of water in one day.

Step-by-step explanation:

Carter drink 15.75 gallons of water in 4 weeks. Each week consists of 7 days, then there are [tex]4\cdot 7=28[/tex] days in for weeks.

If  he drank the same amount of water each day, then he drank in one day

[tex]15.75:28=0.5625[/tex] gallon of water.

Basically here all you want to do it substitute the values x=1 and x=2 for the given function. Use your slope formula [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}  }[/tex].

Do same for x=3 and x=4

You next divide plug in values in to this expression:

[tex]\frac{Slope  of  B}{Slope  of  A}[/tex]

Note how 80 is four times 20. So, 4*4=16. Sam can prepare 80 wall paints in 16 weeks.

Answer:

Its 22

Step-by-step explanation:

By the mid segment theorem:-

3x + 32 = 2(5x + 2)

3x + 32 = 10x + 4

28 = 7x

x = 4

So mid segment = 5(4) = 2 = 22

Answer:

option B

Step-by-step explanation:

To get the graph of piecewise function

We make a table for each function

Plug in end points  and make a table

First function f(x) = (x+2)^2 if x<-1

x <-1 so we pick number for x  less than -1. Also we use -1 but we use open circle at x=-1

x         y = (x+2)^2

-3         (-3+2)^2= 1

-2         (-2+2)^2 = 0

-1           (-1+2)^2 = 1

Now plot the table on graph

second function f(x) = |x| + 1 if -1<=x<=1

Make a table, we use -1, 0  and 1 because we have -1<=x<=1 (-1 and 1 are included)

x        y=|x| +1

-1         |1| + 1 = 2

0        |0|+1 = 1

1          |1|+1= 2

Third function  [tex]y=-\sqrt{x}[/tex]  if x>1

We find out y when x=1 and make a open circle at x=1 because we have x>1

x       [tex]y=-\sqrt{x}[/tex]

1         [tex]-\sqrt{1}=-1[/tex]

4         [tex]-\sqrt{4}=-2[/tex]

Plot all the point on the graph

Correct graph is attached below

Answer: 28 and 18

Step-by-step explanation:

I used the guess and test strategy to find that:  

28 - 10 = 18

28 + 18 = 46

Answer: 3x + 6 -4x = 1

Simplify to -x + 6 = 1 because 3x - 4x = -1x

Answer: The equation will be set up as y=mx+b. Mrs. Jones charges $35 per hour, so we can substitute m for 35 with x representing the number of hours. The $35 for pool usage fee will be substituted for b.

The answer then is y=35x+35

Answer:

Halogens - 6 valence electrons

Step-by-step explanation:

Valence electrons are the number of electrons present in the outermost shell of the atom.

Noble gases have 8 valence electrons which is the maximum and are stable. They are inert by nature since they don't have to combine with any other element to attain stability.

Halogens have 7 valence electrons. They are high electronegative and have great attraction for electrons so that they can attain stability by forming the octet.

The valence electrons in transition metals varies as a group of columns are named transition metals.

Alkali earth metals has two valence electrons.

Hence the incorrect statement here is

Halogens - 6 valence electrons

Answer:

40/81

Step-by-step explanation:

9/25 ÷ 729/1000

We can use copy dot flip

9/25 * 1000/729

I will rewrite to make the math easier

9/729 * 1000/25

9 goes into 729   81 times

1/81 * 1000/25

25 goes into 1000   40 times

1/81 * 40/1

40/81

Answer:

1.6 = x

Step-by-step explanation:

For right angles,   tan x = opposite/adjacent

tan 37 = x / 2.1

Multiply 2.1 on each side.

2.1 tan 37 = x

1.58246 =x

Rounding to the nearest tenth