If the first of three consecutive integers is subtracted from 138, the result is the sum of the second and third. What are the integers?

Answer:

Step-by-step explanation:

we know that

in a right triangle

if sin A= cos B

then

angle A and angle B are complementary angles

so A+B=90

therefore

(7x-15)+(3x+5)=90-----> 10x-10=90----> 10x=100----> x=10°

so

7x-15------> 7*10-15----> 55°

3x+5------> 3*10+5----> 35°

we know that

β < α

therefore

the answer is

β =35°

α=55°

Answer:

34

Step-by-step explanation:

Thats the answer o usatest prep

Answer:

So, if it is translated down 4 units, that puts point d at (-6,5). and after reflecting it over the y axis, that puts it at (6,5). Making the final answer (6,5).

Step-by-step explanation:

The coordinates of point D after being translated four units down and reflected across the Y-axis are (6, 5).

To find the coordinates of point D after the given translation and reflection, we need to perform each step in order.

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Answer is A because when you work it out the area is 110.500 and rounding it makes it -

it is a statistical question due to you having to collect data to answer this question, you'd have to collect data on how tall the giraffes are and i'm sure they all don't grow up to be the same height so there will be differentiations in heights of all.

Answer:

what the other person said

Step-by-step explanation:

Answer:

Answer: A.  Y= -10x -4.

Step-by-step explanation:

Steeper line : is a line which is closed to y-axis, or closed vertically.

Since, the standard form of a line is,

y = mx + c

Where m is the slope,

If the absolute value of the slope ( that is, |m| ) is maximum then it is called it has the steepest graph.

For,  y=-2x+6,

The absolute value of slope = 2,

For, y =8x-1,

The absolute value of slope = 8,

For, y=-10x-4,

The absolute value of slope = 10,

For, Y=7x+3,

The absolute value of slope = 7,

Since, 2< 7 < 8 < 10

Hence, the line y = -10 x - 4 is closest to y-axis,

⇒ Line y = -10 x - 4 has the steepest graph.

A steeper line is one with a greater absolute slope value. Among the provided equations, y = -10x - 4 has the steepest graph due to its absolute slope value of 10.

The correct answer is option A.

A steeper line in the context of linear equations can be understood as a line that is closer to the y-axis or one that has a more significant vertical incline. The steepness of a line is determined by its slope, represented as 'm' in the standard linear equation form, y = mx + c. The slope 'm' quantifies the rate at which the line rises or falls as it moves horizontally along the x-axis. The greater the absolute value of the slope (|m|), the steeper the line.

To identify the steepest line among several equations, one must calculate and compare the absolute values of their slopes. Let's evaluate a few examples:

For y = -2x + 6, the absolute value of the slope is |2|.

For y = 8x - 1, the absolute value of the slope is |8|.

For y = -10x - 4, the absolute value of the slope is |10|.

For y = 7x + 3, the absolute value of the slope is |7|.

Comparing these absolute values, we find that 2 < 7 < 8 < 10. Therefore, the line with the steepest graph is y = -10x - 4. This line is closest to the y-axis, indicating the most significant vertical incline among the given equations.

Therefore, from the given options the correct one is A.

For more such information on: absolute slope value

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Answer:

600 cocoa beans

Step-by-step explanation:

because pounds and lb is that same thing and for 3 pounds of chocolate, you need 600 cocoa beans

200 cocoa beans makes 1 pound of chocolate.

Since,

1 multiplied to 3 is 3.

So,

200x3 cocoa beans make 1 pound of chocolate.

=600 cocoa beans

Therefore 600 cocoa beans make 3 pounds of chocolate.

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=8\\ h=4 \end{cases}\implies 8=\cfrac{1}{2}b(4)\implies 8=2b\implies \cfrac{8}{2}=b\implies 4=b[/tex]

To find the length of the base of a triangle with an area of 8 square feet and a height of 4 feet, you rearrange the formula for the area of a triangle and solve for the base, resulting in a base length of 4 feet.

The question asks for the length of the base of a triangle given that the area is 8 square feet and the height is 4 feet. To find the base of the triangle, we can rearrange the formula for the area of a triangle, which is A = (1/2) * base * height. Substituting in the given values and solving for the base, we get:

Base = (2 * Area) / Height

Next, we replace the values for Area and Height:

Base = (2 * 8 sq ft) / 4 ft

Base = 16 sq ft / 4 ft

Base = 4 feet

Therefore, the length of the base of the triangle is 4 feet.

Distributed property because this property allows u two put 4r+2r because this equation is also (4xr)+(2xr) since they have the same variable u can put them together 4+2 is 6 and then just multiply by r so it’s 6r. And let’s not forget about 3s it doesn’t have the same variable so you can do 6r+3s which is what u got and is the correct answer 6r+3s is simplified but it’s the same as 4r+3s+2r

Answer:

[tex]P =0.857[/tex]

Step-by-step explanation:

We know that 60% of students have an iPad and a car and 70% have a car.

If we call A the event "have an iPad" and call the event B "have a car"

So

[tex]P (A\ and\ B) = 0.6\\\\P(B) = 0.7[/tex]

We look for the probability that a student with a car also has an iPad. This is

[tex]P (A | B) = \frac{P(A\ and\ B)}{P(B)}\\\\P (A | B) = \frac{0.6}{0.7}\\\\P (A | B) = 0.857[/tex]

Answer:

86%

Step-by-step explanation:

To solve this problem you need to use the formula for conditional probability.  

P(Ipod|Car) = P(Car and Ipod)P(Car).

P(a student with a car also has an iPod) = 0.6/0.7 = 0.857 = 86%

Answer:

The answer to Number 21 is A

The cyclist's speed converts to 43.2 km/h. In 3 hours, she will travel a distance of 129.6 kilometers.

The rate of the cyclist in kilometers per hour can be calculated by converting meters per second to kilometers per hour. To do this, we multiply the speed in meters per second by 3.6 (since 1 m/s = 3.6 km/h). Thus, the cyclist's speed in km/h is 12 m/s * 3.6 = 43.2 km/h.

To calculate the distance she will travel in 3 hours, we multiply the speed (in km/h) by the time in hours. So, the distance is 43.2 km/h * 3 hours = 129.6 km.

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The cyclist's rate in kilometers per hour is 43.2 km/h, and she will travel 129.6 km in 3 hours.

To convert the rate from meters per second (m/s) to kilometers per hour (km/h), we need to use conversion factors.

Conversion factors:

1 m/s = 3.6 km/h

1 hour = 3600 seconds

Let's calculate:

Rate in km/h = (Rate in m/s) × (Conversion factor from m/s to km/h)

Rate in km/h = 12 m/s × 3.6 km/h

Rate in km/h = 43.2 km/h

To calculate the distance traveled in 3 hours, we can use the formula:

Distance traveled = Rate × Time

Distance traveled = 43.2 km/h × 3 hours

Distance traveled = 129.6 km

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Answer:

Step-by-step explanation

round the numbers so it is easier to work with

10 * 7 = 70

70 * 7 = 490

20 * 7 = 140

140 *7 = 980

980 + 490 = 147.0

The total amount that Diego could have spent on lunch over the past seven weeks could be between $77 and $119.

To determine the total amount Diego could have spent on lunch over the past seven weeks, you should find the minimum and maximum amounts he could have spent. The minimum amount would be if he spent $11 each week, and the maximum if he spent $17 each week.

To find these amounts, you multiply the number of weeks by the respective cost. So, for the minimum, you multiply 7 weeks by $11, which gives a total of $77. Then, for the maximum, you multiply 7 weeks by $17, which gives a total of $119.

Therefore, the total amount that he spent on lunch for the past 7 weeks could be any amount between $77 and $119.

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Answer: Option A

[tex]A=0.001[/tex]

Step-by-step explanation:

The sinusoidal functions have the following form

[tex]Y = Asin (bx)[/tex]

Where

[tex]\frac{2\pi}{b}[/tex] is the period of the function

A is the amplitude: Half the difference between the minimum value and the maximum value of the function.

In this case the function is:

[tex]y = 0.001sin(880\pi\phi)[/tex]

Therefore the amplitude of this equation is [tex]A=0.001[/tex]

Let's talk about what we do know, before we answer the question.

Probability =  (1/2)^5 x (1/2) = 1/64 or 1.5625%, which rounds to -

1.6% [C] <----------

Final answer:

The probability of tails coming up on the 6th flip of a coin is calculated as (0.5)^6, which equals 0.015625 or 1.6% after rounding to the nearest tenth of a percent.

Explanation:

To calculate the probability of tails coming up on the 6th flip of a coin, we must first understand that each flip of a fair coin is an independent event with two possible outcomes: heads or tails. The probability for each of these outcomes on a single flip is 50% or 0.5. In order for tails to come up on the 6th flip specifically, we need to have five heads before that. The probability of getting heads five times in a row is (0.5)^5, and then we multiply this by 0.5 again for the probability of the 6th flip being tails. Hence, the calculation is (0.5)^6.
(0.5)^6 = 0.015625, which is the same as 1.5625%. Rounding this to the nearest tenth of a percent, the probability of tails coming up on the 6th flip is 1.6%, which corresponds to option C.

2⃣, -4⃣ = x; no radical necessary.

Answer:  D. A pentagon

According given statement Ragan drew pentagon. Therefore, option D is the correct answer.

A pentagon is a five-sided polygon with five straight sides and five angles. It is a regular polygon, meaning all of its sides are equal in length and all of its angles are equal in measure.

Given that, Ragan drew a polygon with more than a square and fewer vertices than a hexagon.

We know that, square has 4 sides and a hexagon has 6 sides.

According to statement, Ragan drew pentagon.

Therefore, option D is the correct answer.

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Answer:

[tex]\$189.50[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\ P=\$175\\ r=0.04\\n=4[/tex]  

substitute in the formula above  

[tex]A=\$175(1+\frac{0.04}{4})^{4*2}=\$189.50[/tex]  

5950 have been bullied in that particular school of 7000

Seems like you had your minus signs backwards. Try y = 3 and y = -6

1/6 < 1/4 so 1/6 would equal 2/12 and 1/4 would equal 3/12 so which means if you take one from each it would be 5/12 but if you took 2 from the first one it would only be 2/12 which is why you need to read correctly because THE REASON MARK IS CORRECT IS BECAUSE 5/12 IS GREATER THAN 2/12

Answer:

Step-by-step explanation:

From 1:45 to 4:00 is:

15 min to 2:00

from 2:00 to 4:00 is 2h

We know 1h = 60min, therefore 1min = 1/60 h

2h and 15min = 2h + 15/60 h = 2h + 1/4 h = 2 1/4h = 2.25h

Answer:

y > -1/3x - 1

Step-by-step explanation:

The inequality is a linear inequality whose equation can be written using a form similar to y = mx + b. Remember m is the slope and b is the y-intercept. Here the line crosses the y-axis at b = -1. And it has as a slope m = -1/3. The equation is then y = -1/3x - 1. Since this is an inequality with a dashed line then the symbols <,> must replace the =. There are two options:

y < -1/3x - 1 and y > -1/3x - 1

Test the point (0,0) which is in the solution set to determine which equation holds true.

0 < -1 and 0 > -1

The first is false and the second is true. The correct equation is y > -1/3x - 1

QUESTION 1

The point-slope form equation of a line is given by:

[tex]y-y_1=m(x-x_1)[/tex]

Given slope:

[tex]m = \frac{2}{3} [/tex]

and point:(-3,5)

The point-slope form equation is:

[tex]y-5= \frac{2}{3} (x- - 3)[/tex]

This simplifies to:

[tex]y-5= \frac{2}{3} (x + 3)[/tex]

The correct option is D.

QUESTION 2

We use any two points from the table to find the required equation.

(2,14) and (4,23)

The slope is given by the formula,

[tex]m = \frac{23 - 14}{4 - 2} = \frac{9}{2} [/tex]

The equation is given by;

[tex]y-y_1=m(x-x_1)[/tex]

We plug in values to get;

[tex]y-14= \frac{9}{2} (x-2)[/tex]

Expand:

[tex]y = \frac{9}{2} x - 9 + 14[/tex]

The slope-intercept form is:

[tex]y = \frac{9}{2} x + 5[/tex]

The correct choice is B

ANSWER

[tex]\cos( \theta) = - \frac{5\sqrt{61}}{ 61 } [/tex]

EXPLANATION

The given point is (-5,-6).

This implies that ,

[tex] \tan( \theta) = \frac{6}{5} [/tex]

Hence opposite=6 units and adjacent=5 units.

The hypotenuse is,

[tex] = \sqrt{ {5}^{2} + {6}^{2} } = \sqrt{61} [/tex]

Since the terminal side is in the third quadrant, the cosine ratio is negative.

[tex] \cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = - \frac{5}{ \sqrt{61} } [/tex]

Rationalize the denominator,

[tex]\cos( \theta) = - \frac{5\sqrt{61}}{ 61 } [/tex]

The correct choice is C.

Answer:

Step-by-step explanation:

g(x) = x^2 - x

g(2/3) = (2/3)^2 - 2\3 = 4/9 - 2/3 = 4/9 - 6/9 = -2/9

Answer:

-2/9

Step-by-step explanation:

g(x) = x² - x

Substitute x = 2/3 into g(x).

g(2/3)

= (2/3)²  - (2/3)

= 4/9 - 2/3

= 4/9 - 6/9

= -2/9

Answer:

A,C, AND D

Step-by-step explanation:

A. 3+4>5 therefore a triangle

B. 1+7<10 therefore not a triangle

C. 1.5+1.5>2.5 therefore a triangle

D. 7+7>7 therefore a triangle

E. 6+6=12 therefore not a triangle

Answer:

The glue stick with 3/8

Step-by-step explanation: if you make the denominators for both equations the same 1/5 would turn into 8/40 and 3/8 would turn into 15/40. This means that 3/8 would be 7% bigger  

The second glue stick has [tex]\( \frac{7}{40} \)[/tex] more glue than the first glue stick.

To compare the amount of glue left in each glue stick, we need to find a common denominator for [tex]\( \frac{1}{5} \)[/tex] and [tex]\( \frac{3}{8} \)[/tex].

The least common denominator (LCD) for 5 and 8 is 40.

Now, let's rewrite [tex]\( \frac{1}{5} \)[/tex] and [tex]\( \frac{3}{8} \)[/tex] with the common denominator of 40:

[tex]\[ \frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40} \]\[ \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \][/tex]

Now, we can compare the amounts:

- Glue stick 1: [tex]\( \frac{8}{40} \)[/tex] left.

- Glue stick 2: [tex]\( \frac{15}{40} \)[/tex] left.

Since [tex]\( \frac{15}{40} \)[/tex]is greater than [tex]\( \frac{8}{40} \)[/tex], the second glue stick has more glue left.

Alternatively, we can also subtract the fractions to find the difference:

[tex]\[ \frac{15}{40} - \frac{8}{40} = \frac{15 - 8}{40} = \frac{7}{40} \][/tex]

Answer:

-  The lines of both functions have the same slope.

- The line of the first function intercepts the y-axis at the point (0,-6) and the  line of the new function intercepts the y-axis at the point (0,-8).

- The new graph is the graph of the first function but shifted 2 units down.

Step-by-step explanation:

The equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function in the form [tex]y=x-6[/tex], you can identify that:

[tex]m=1\\b=-6[/tex]

And from the new function in the form  [tex]y=x-8[/tex], you can identify that:

[tex]m=1\\b=-8[/tex]

This means that the lines of both functions have the same slope, but the line of the first function  [tex]y=x-6[/tex] intercepts the y-axis at the point (0,-6) and the  line of the new function  [tex]y=x-8[/tex] intercepts the y-axis at the point (0,-8).

Therefore, the graph of the new function is 2 units below of the function [tex]y=x-6[/tex], or, in other words, the new graph is the graph of the first function but shifted 2 units down.

For reference,

[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]

a. [tex]\dbinom{52}5=2,598,960[/tex] - nothing special here, you're just choosing any 5 cards from the deck

b. [tex]\dbinom{13}4\dbinom{39}1=27,885[/tex] - 13 hearts to choose from, and 39 of any other suit

c. [tex]\dbinom{40}5=658,008[/tex] - there are 12 face cards to omit from the count

d. [tex]\dbinom{26}5=65,780[/tex] - half the deck contains spades/clubs

e. [tex]\dbinom{26}5=65,780[/tex] - essentially the same situtation as (d)

f. [tex]\dbinom{40}5\dbinom{12}0+\dbinom{40}4\dbinom{12}1+\dbinom{40}3\dbinom{12}2=2,406,768[/tex] - either 0, 1, or 2 face cards are allowed

g. [tex]\dbinom{13}2\dbinom{39}3+\dbinom{13}3\dbinom{39}2+\dbinom{13}4\dbinom{39}1+\dbinom{13}5\dbinom{39}0=953,940[/tex] - similar to (f)

A) Total Different Hands=2,598,960

B) Hands Containing 4 Hearts=27,885

C) Hands Containing No Face Cards=658,008

D) Hands Containing Only Spades or Only Clubs=2,574

E) Hands Containing Only Red Cards=65,780

F) Hands Containing No More Than 2 Face Cards= 915528

G) Hands Containing At Least 2 Hearts=1,894,929

This problem involves calculating the number of different hands possible when dealing five cards from a standard deck of 52 playing cards.

We also need to determine the count for various specific conditions.

A) Total Different Hands

To determine the number of different hands, we use the combination formula C(n, k) where n is the total number of items, and k is the number of items to choose.

For our case:

C(52, 5) = 52! / (5!(52-5)!) = 2,598,960

B) Hands Containing 4 Hearts

We select 4 hearts from the 13 available and the 5th card from the remaining 39 cards:

C(13, 4) * C(39, 1) = 715 * 39 = 27,885

C) Hands Containing No Face Cards

There are 40 non-face cards (4 suits each with A-10). Thus, the number of ways to select a 5-card hand with no face cards is:

C(40, 5) = 658,008

D) Hands Containing Only Spades or Only Clubs

Since we can't mix suits, we compute separately and add:

C(13, 5) * 2 (one for each suit) = 1,287 * 2 = 2,574

E) Hands Containing Only Red Cards

There are 26 red cards (hearts and diamonds), so we choose from these:

C(26, 5) = 65,780

F) Hands Containing No More Than 2 Face Cards

Calculating for 0, 1, and 2 face cards separately:

Total=C(40, 5) + C(12, 1) * C(40, 4) + C(12, 2) * C(40, 3) = 658,008 + 114,960 + 142,560 = 915528

G) Hands Containing At Least 2 Hearts

We use the complement rule: subtract the combinations with 0 or 1 heart from the total:

Total=C(52, 5) - (C(39, 5) + C(13, 1) * C(39, 4)) = 2,598,960 - (575,757 + 128,274) = 1,894,929