The sum of two consecutive integers is 5.
What are the numbers?
Hint. Consecutive integers differ by 1,
so let x = smaller integer and y = x + 1 =
next larger.

The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9

The arithmetic sequence is given as:

a₁, a₂ and a₃

The geometric sequence is given as:

a₄, a₇ and a₁₂

The common ratio of a geometric sequence is:

[tex]r = \frac{T_2}{T_1}[/tex]

So,we have:

[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]

Cross multiply

[tex]a_{12} * a_4 = a_7 * a_7[/tex]

Given that a7 = 30, the equation becomes

[tex]a_{12} * a_4 = 30 * 30[/tex]

Evaluate the product

[tex]a_{12} * a_4 = 900[/tex]

Rewrite as:

[tex]a_{4} * a_{12} = 900[/tex]

Express 900 as 10 * 90

[tex]a_{4} * a_{12} = 10 * 90[/tex]

By comparison, we have:

a₄ = 10 and a₁₂ = 90

This means that the geometric sequence is:

10, 30, 90 ---- it has a common ratio of 3

The nth term of a geometric sequence is:

[tex]a_n = ar^{n-1}[/tex]

So, we have:

[tex]a_7 = ar^6[/tex]

[tex]a_4 = ar^3[/tex]

Substitute values for a7 and 14

[tex]ar^6 = 30[/tex]

[tex]ar^4 = 10[/tex]

Divide both equations

[tex]r^2 = 3[/tex]

Take the cube of both sides

[tex]r^6 = 27[/tex]

Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]

[tex]a * 27 = 30[/tex]

Divide both sides by 27

[tex]a = \frac{10}{9}[/tex]

Hence, the value of a1 in the geometric sequence is 10/9

Read more about sequence at:

https://brainly.com/question/7882626

#SPJ1

Answer:

0.3386 = 0.339 (rounded).

Step-by-step explanation:

It is the binomial type probability distribution.

The number of trial n= 3; the probability of the success trial is  0.16,  and the number of success trial k = 1.

Answer:

42

Step-by-step explanation:

You turn the percentage into a decimal, 25%=0.25

then you multiply 0.25 to 168

Then you get 42

0.25 x 168 = 42

Hope this helps <3

Area of centre rectangle

Area of right rectangle

Area of triangle

Total

Answer:

B. 60

Step-by-step explanation:

1. take the square root of 64

2. multiply 8*10 and 5*4

3. subtract

Square root of 64 is 8 so,

10*8 - 5*4

80 - 20 =

60

Step-by-step explanation:

first of all, all answer options are basically wrong, because an area is always measured in units² (and not just in units).

the blue colored area is the area of the whole square minus the area of the circle.

the side length of the square is 2 times the radius of the circle (the diameter) : 2×12 = 24 units.

so, the area of the square is

24² = 576 units²

the are of the circle is

pi×r² = pi×12² = 144pi units²

so, the blue area is

576 - 144pi = 123.6106579... ≈ 124 units²

therefore, D is the right answer.

A composite transformation is the production of the image of a figure through two or more transformation

The set of transformations that could be applied to rectangle ABCD to create rectangle A'B'C'D' is the second option;

The reason the above selected option is correct is as follows:

Known parameters:

The given coordinates of the vertices of the preimage of the rectangle ABCD are; A(-4, 2), B(-4, 1), C(-1, 1), and D(-1, 2)

The given coordinates of the vertices of the image of the rectangle ABCD, which is rectangle A'B'C'D' are; A'(-4, -2), B'(-4, -1), C'(-1, -1), and D'(-1, -2)

Solution:

The form of the ordered pair of the vertices of the pre-image is negative value for x, positive value for y, which can be written as (-x, y), where x, and y, are positive numbers

The form of the ordered pair of the vertices of the image is (-x, -y)

The location of a point (-x, y) following a reflection over the y-axis is the point (x, y)

The location of a point (x, y) following a 180° rotation is the point (-x, -y)

Therefore, the set of transformations that can be applied to (-x, y), to create (-x, -y), is a reflection over the y-axis, followed by a rotation of 180

Which gives;

Therefore, the correct option is; Reflected over the y-axis and rotated 180°

Learn more about composite transformations here:

https://brainly.com/question/12906823

https://brainly.com/question/14274933

Answer: B is your correct answer!

Step-by-step explanation:

Answer:

$19.29

Step-by-step explanation:

there you have it

Answer:

The answer is D.

Step-by-step explanation:

f(x) = 5x -3

y = 5x - 3

Switch y and x to find the inverse

x = 5y - 3

Solve for y.

x + 3 = 5y

y = (x+3)/5

g(x) = (x+3)/5

To solve this problem, we have to figure out the time spent travelling and then use the speed-distance-time equation to find the distance between the two places. The distance between Seattle and St. Louis is 2295 miles.

To calculate the miles or distance between Seattle and St. Louis, we have to take into consideration that out of the 42 hours she spent in her journey, she stayed 15 hours over at St. Louis.

[tex]42 - 15 = 27[/tex]

She spent 27 hours travelling.

Her speed in the first journey was 50mi/h and her speed in the second journey was 35mi/h.

This implies she was faster in her first journey compared to her second journey.

Data;

[tex]speed = \frac{distance}{time} \\distance = speed * time[/tex]

Let's substitute the values

[tex]distance = (50 + 35) * 27 = 2295mi[/tex]

The distance between Seattle and St. Louis is 2295 miles

Learn more on distance, speed and time here;

https://brainly.com/question/24571540

#SPJ1

Answer:

The question is asking you to subtract 516 from 1,000 to find b.

[tex]1,000 - 516 = 484[/tex]

Therefore, b = 484

[tex] \bold{\underline{\underline{\underbrace{Answer}}}} [/tex]

x = a and y = b

Step-by-step explanation:

The value of x and y

⠀

ax + by = a² + b² (equation 1)

bx - ay = 0 (equation 2)

⠀

{Taking equation 2}

[tex] \sf bx - ay = 0 [/tex]

{Taking ay on RHS}

[tex] \sf bx = ay[/tex]

{Dividing both sides by a}

[tex] \sf \frac{bx}{a} = y(equation \: 3)[/tex]

{Now substituting the equation 3 in equation 1}

[tex] \sf ax + b( \frac{bx}{a} ) = {a}^{2} + {b}^{2} \\ \\ \sf ax + \frac{ {b}^{2} x}{a} = {a}^{2} + {b}^{2} [/tex]

{Taking LCM on LHS}

[tex] \sf \frac{ {a}^{2}x + {b}^{2} x }{a} = {a}^{2} + {b}^{2} \\ \\ \sf \frac{x( {a}^{2} + {b}^{2}) }{a} = ( {a}^{2} + {b}^{2} )[/tex]

{Dividing by (a² + b²) both sides}

[tex] \sf \frac{x}{a} = 1 \\ \\ \green{\boxed {\tt{x = a} } }[/tex]

{Now substituting the value of x in equation 3}

[tex] \sf \frac{ba}{a} = y \\ \\ \green {\boxed{ \tt{y = b}} }[/tex]

See the file attached!!

Hope it helps:)

Answer:

The area is 9 units^2

Step-by-step explanation:

Based on the number of ways to answer the multiple choice questions and the number of ways to answer true or false, the number of ways to answer the test is 8,192 ways.

This can be found as:

= Total number of ways to answer multiple choice questions + Total ways to answer true or false questions

Solving gives:
= (4 x 4 x 4) x (2 x2 x2 x 2 x 2 x 2 x 2)

= 64 x 128

= 8,192 ways

Find out more on the number of ways to do things at https://brainly.com/question/4658834.

#SPJ1

Answer:

x is -1  

Step-by-step explanation:

-4 multiplied by x is -4x, then -4 x 3 is -12, which makes the problem -4x + -12  and you need to do the opposite so  add 4, -4x cancels out and then add 4 to -12 which is 8x

Answer:

28 times

Step-by-step explanation:

On a fair die, the probability of rolling a 6, the only number greater than 5, is 1/6. So in 168 rolls of this die, Malachy can expect a 6 on 1/6 × 168, or 28 times.

Answer:

the answer is 126 cm

sana makatulong

Answer:

2¹² Bytes

Step-by-step explanation:

One kilobyte is 2¹⁰ bytes.

File size of the email is 4 kilobytes. That is 4 times 1 kilobyte. Therefore multiply with 4.

4 KB = 4 × 2¹⁰ B

Now notice that you can rewrite 4 like 2².

4 KB = 2² × 2¹⁰ B

Use exponental rule (Product Rule):

[tex]a^x + a^y = a^{x+y}[/tex]

4 KB = 2²⁺¹⁰ B = 2¹² B

Answer:

i think the answer is X, because the elements of both X and Y are in X

Answer:

should be 1305 yd^2

Step-by-step explanation:

to get the surface area of one of the 3 recanglular sides take 24 x 15 to get 360 then muliply by 3 to get 1080 since all the recanglular sides are the same then do 15 x 15 to get both of the triangle sides to get 225 since the equation is 1/2 B x H then add them together

Answer:

Since the 'base' and 'top' of any prism have the same shape, the surface area can be found by

surface area of prism = 2 * area of base + perimeter of base * H

So for the rectangular prism in your example..

surface area = 2LW + 2(L+W)H

= 2 * 7 * 4 + 2*(7+4)*5

= 56 + 2 * 11 * 5

= 56 +110

= 166 sq cm

Hope this helps

Answer:

95

Step-by-step explanation:

Surface Area :

⇒ Area (4 triangle faces) + Area (square base)

⇒ 4 x 1/2 x 5 x 7 + (5)²

⇒ 2 x 35 + 25

⇒ 70 + 25

⇒ 95 square centimeters

Answer: C

Step-by-step explanation: bcuz

Answer:

[tex]\textsf{A)} \quad f\left(-\dfrac{1}{2}x\right)[/tex]

Step-by-step explanation:

From observation of the given graph, function f has been reflected across the y-axis.  

When a graph is reflected across the y-axis, the y-coordinate stays the same while the x-coordinate is negated.

Therefore, replace y = f(x) with y = f(-x), so:

[tex]\implies g(x) = f(-x)[/tex]

It appears that the graph has also been stretched parallel to the x-axis.

When a graph is stretched parallel to the x-axis the x is multiplied by a constant.  If the constant is greater than 1, the graph is compressed.  If the constant is greater than zero and less than 1, the graph is stretched.

As the graph has been stretched, the constant is 0 < c < 1, so:

[tex]\implies g(x)=f\left(-\dfrac{1}{2}x\right)[/tex]

Answer:

2/3

Step-by-step explanation:

total marbles is (8 black+ 16 white + 14 red +10 green) = 48

no white cmarbles ( 8+14+10) = 32

32/ 48 =  2/3

The first two terms of the sequence are 3 and 12 and the 3rd and 4th terms are 25 and 42.

The 3rd and 4th terms of the sequence is determined from second level difference as shown below;

(c - b) - (b - a) = 4  ----(1)

(d - c) - (c - b) = 4 ---- (2)

from (1);

(c - 12) - (12 - 3) = 4

(c - 12) - (9) = 4

c - 21 = 4

c = 25

from (2);

(d - 25) - (25 - 12) = 4

d - 38 = 4

d = 42

The sequence = 3, 12, 25, 42

check

first difference = (12 - 3), (25-12), (42-25) = 9, 13, 17

second difference = (13 - 9), (17 - 13) = 4, 4

Thus, the first two terms of the sequence are 3 and 12 and the 3rd and 4th terms are 25 and 42.

Learn more about sequence here: https://brainly.com/question/6561461

#SPJ1

The value for the test statistic and the p value on the test when the researcher wanted to see if different breeds of dogs will be x² = 0.9421 and 0.05 < p value < 0.10.

From the information given, the null hypothesis is that the variables have no difference while the alternative hypothesis is that they have a difference.

The degree of freedom will be:

= (3 - 1) × (3 - 1)

= 4

The critical value is 9.4877. In this case, the p value is greater than the significance level. Therefore, we fail to reject the null hypothesis.

Learn more about research on:

https://brainly.com/question/968894

#SPJ1

Answer:

Step-by-step explanation:

From Khan

Answer:

Ok I can walk you through if you comment the questions ok?

Step-by-step explanation:

Trust me :-)

Answer:

1. obtuse

2.straight

3.right

4. acute

5. <EAF

6. <DAF

7. <BAF

8. They are perpendicular to each other