x+4y=16
5x+4y=0
need to solve systems of equations by graphing

Answer:

1. 23.55 in

2. 102.36 mm

Step-by-step explanation:

First, the circumference of a circle is written as: [tex]C=\pi d=2\pi r[/tex], where either equivalence works and d = diameter and r = radius.

1. We know that d = 7.5, so we just plug this into the equation:

[tex]C=\pi *7.5=3.14*7.5=23.55[/tex]

Thus, the circumference is 23.55 inches.

2. We know here that r = 16.3, so we can plug this into the other equivalence:

[tex]C=2*\pi *16.3=2*3.14*16.3=102.364[/tex] ≈ [tex]102.36[/tex]

Thus, the circumference is 102.36 millimeters.

Hope this helps!

Answer:

1. 23.55 inches

2. 102.36 millimeters

Step-by-step explanation:

1. Circumference = pi × d

3.14 × 7.5

= 23.55 in

2. Circumference = 2pi × r

2 × 3.15 × 16.3 = 102.364 mm

Answer:

The answer to your question is   b = 11.31 cm  or   8[tex]\sqrt{2}[/tex] cm

Step-by-step explanation:

Data

hypotenuse = 18 cm

one leg = 14 cm

second leg = ?

Process

1.- Use the Pythagorean Theorem to solve this problem

                 c² = a² + b²

c = hypotenuse

a = longer leg

b= shorter leg

2.- Substitution

                        18² = 14² + b²

-Solve for b

                         b² = 18² - 14²

-Simplify

                         b² = 324 - 196

                         b² = 128

-Find the prime factors of 128

                          128   2

                            64  2

                             32  2

                             16  2

                              8  2

                              4  2

                              2  2

                               1

          128 = 2⁶2¹                                    

-Result

                         b = 11.31   or   8[tex]\sqrt{2}[/tex]

Answer:

21.32 Cm

Step-by-step explanation:

Add up the centiminer

Answer:

15 and 16

Step-by-step explanation:   To get simplified form, you add the numbers in parentheses together. (2+9+4)= 15 and (3+1+4+8)=16

For problem 1. 2+9=11  11+4=15

For problem 2. 3+1=4    4+4=8   8+8=16

Hopefully this helped, and please add me as brainliest.

Final answer:

The simplified forms of the expressions (2 + 9 + 4) and (3 + 1 + 4 + 8) are 15 and 16, respectively. The placement of parentheses affects the outcome of mathematical operations significantly, and careful evaluation following the order of operations is essential for accurate simplification, particularly when nested expressions are involved.

Explanation:

The question requires matching each mathematical expression with its simplified form. Let's simplify the given expressions:

(2 + 9 + 4) simplifies to 2 + 9 + 4 = 15.

(3 + 1 + 4 + 8) simplifies to 3 + 1 + 4 + 8 = 16.

Now, to address your example concerning the importance of the placement of parentheses, consider the expression 2 + (3 x 5). If the parentheses are around (2 + 3), the result is different than if the parentheses are around (3 x 5). Without any parentheses, the order of operations dictates that multiplication is done before addition. Hence:

(2 + 3) x 5 = 5 x 5 = 25 (since addition within parentheses is done first, followed by multiplication).

2 + (3 x 5) = 2 + 15 = 17 (since multiplication within parentheses is done first, followed by addition).

Answer:

375

Step-by-step explanation:500 equals 100% divide by 4 its 125 times 3 equals 375, your welcome

Answer:

They will need 375 hamburgers.

Step-by-step explanation:

Keeping the ratio in mind, we solve this problem by cross multiplying. Set up the ratio 4/3 and set it equal to the greater ratio of 500/(an unknown number of hamburgers, represented by x). Cross multiply to end up with the equation 4x=1500. (Cross multiplying is multiplying each numerator by the opposite denominator). Solve for x in the above equation using SADMEG. You divide 1500 by 4 and end up with 375 hamburgers.

The answer would be D since it forms a straight line along the x-axis

A 99% confidence interval for the mean body temperature can be calculated using the sample mean, standard deviation, and the t-score corresponding to the confidence level. The findings may suggest that the commonly accepted average body temperature of 98.6°F could be reconsidered if it does not fall within this interval.

Constructing a 99% Confidence Interval

To construct a 99% confidence interval for the mean body temperature of all healthy humans, we use the sample mean, standard deviation, and the t-distribution since the population standard deviation is not known. With a mean of 98.9°F, a standard deviation of 0.67°F, and a sample size of 103, we can calculate the margin of error using a t-score that corresponds to the 99% confidence level.

First, we find the t-score from the t-distribution table for 102 degrees of freedom (n-1) that corresponds to a 99% confidence level. Then, we calculate the margin of error using the formula:

Margin of Error (E) = t-score * (standard deviation / sqrt(n))

This margin of error is then added and subtracted from the sample mean to obtain the confidence interval:

Lower Limit = Mean - Margin of Error

Upper Limit = Mean + Margin of Error

This confidence interval provides a range within which we can be 99% confident that the true mean body temperature of all healthy humans lies.

Implications for 98.6°F as Average Body Temperature

The sample suggests that the mean body temperature of 98.6°F might not be accurate for all individuals. If the constructed 99% confidence interval does not contain the traditional mean of 98.6°F, it could indicate that the average body temperature is different than what has been historically taught.

The 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.

To construct a 99% confidence interval for the mean body temperature of all healthy humans, we'll use the formula:

[tex]\[ \text{Confidence Interval} = \bar{x} \pm z \left( \frac{s}{\sqrt{n}} \right) \][/tex]

Let's calculate the confidence interval:

[tex]\[ \text{Confidence Interval} = 98.9 \pm 2.576 \left( \frac{0.67}{\sqrt{103}} \right) \]First, let's calculate \(\frac{s}{\sqrt{n}}\):\[ \frac{s}{\sqrt{n}} = \frac{0.67}{\sqrt{103}} \approx 0.0662 \][/tex]

Now, we can find the margin of error:

[tex]\[ \text{Margin of Error} = 2.576 \times 0.0662 \approx 0.1706 \]Finally, construct the confidence interval:\[ \text{Confidence Interval} = 98.9 \pm 0.1706 \][/tex]

So, the 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.

Final answer:

Option D, with scores of 100, 87, 94, 94, and 81, yields the highest average when calculated using the mean, making it the best choice for the student seeking the highest test average.

Explanation:

The question asks which set of test scores will give the highest average if calculated using the mean. To find the answer, we calculate the mean of each set of scores:

A: (95+82+76+95+96)/5 = 88.8

B: (79+80+91+83+80)/5 = 82.6

C: (65+84+75+74+65)/5 = 72.6

D: (100+87+94+94+81)/5 = 91.2

Among the options, option D has the highest mean.

Therefore, the student with test scores of 100, 87, 94, 94, and 81 will have the highest average when using the mean to calculate.

Answer:

Option 2 is correct

Since only 18 is less than 23 and greater than 7, therefore the possible length of third sides is 18 cm and option 2 is correct.

Answer:

130.43 cm³

Step-by-step explanation:

To find the difference between the volumes of the balls, we must first find the volumes of the balls. To find the volume of each ball, we must first determine their shape. We understand that both balls are spherical.

The volume V of a sphere wit radius r is given as

V = 4/3 πr³

where r is the result when the diameter of the sphere is divided by 2.

Hence the radius of the Golf ball

= 4.3cm/2

= 2.15cm

radius of the tennis ball

= 6.9cm/2

= 3.45cm

The difference between the volumes of the two balls

= 4/3 π (3.45³ - 2.15³)

= 130.43 cm³

Answer:

No

Step-by-step explanation:

For it to be a triangle c² = a² + b²

The longest side is c (9)

and 81 ≠ 49 + 16

Can I get brainliest

Answer:

No

Step-by-step explanation:

Since it might be a right triangle, we can test the values using the Pythagorean theorem.

[tex]a^2+b^2=c^2[/tex]

a and b are the legs, and c is the hypotenuse.

We know that 4 and 7 are the legs, or a and b. This is because they are two smaller sides.  We know that 9 is the hypotenuse, or c. This is because it is the longest side.

[tex]4^2+7^2=8^2[/tex]

Solve the exponents

[tex]16+49=81[/tex]

65=81

[tex]65 \neq 81[/tex]

Since 65 does not equal 81, this cannot be a right triangle

Answer:

A, C and D are correct.

\

Step-by-step explanation:

A is correct.

B is false; that space is the "area" of the circle.

C is true.  C = πd

D is true.  C = 2πr

E is false.  Way off.

Final answer:

Circumference is the distance around a circle, calculated as C = πd or C = 2πr, depending on whether the diameter or radius is known. (Option A,C,D)

Explanation:

Circumference is the term used to describe the distance around a circle. When calculating the circumference, you can use different formulas depending on the information you have about the circle. If you know the diameter (d), the circumference (C) can be found by multiplying the diameter by pi (π), using the formula C = πd. Alternatively, if you know the radius (r) of the circle, you can use the formula C = 2πr since the diameter is twice the radius (d = 2r).

The correct answers to the question are:

It's important to note that the space inside the circle is referred to as the area, not the circumference, and the formula for circumference is not C = pi + r as stated in option E, but rather C = πd or C = 2πr.

Answer:

  A)  33 3/4°

Step-by-step explanation:

The supplement of an angle is the difference between 180° and the angle measure:

  supplement of 146 1/4° = 180° -(146 1/4)°

  = (180° -146°) -1/4° = 34° -1/4°

  = 33 3/4° . . . . supplement of the given angle

The width of the computer monitor is 22 inches

What is a Rectangle?

In a Rectangle

The diagonal equals the square root of the width squared plus the height squared

Given data ,

Let the Width of the rectangle be W

Diagonal of the rectangle = 27 inches

Height of the rectangle = 15 inches

D² = L² + W²

W² = D² - L²

W² = ( 27 )² - ( 15 )²

     = 729 - 225

     = 504

Therefore , Width W = √504

                                  ≈ 22.45 inches

                                  ≈ 22 inches

Hence , the width of the computer monitor is 22 inches

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Answer:

this is to much work for me to do.

Step-by-step explanation:

Answer: True

Explanation: To add mixed numbers, first add the fractions.

So here, we have 4/9 + 6/9 which is 10/9.

Then add the whole numbers.

So we have 1 + 2 which is 3.

So our answer is 3 and 10/9.

But notice, that since 10/9 is an improper fraction,

our answer is not in lowest terms.

10/9 can be rewritten as the mixed number 1 and 1/9.

So 3 and 10/9 is the same as 3 + 1 and 1/9 which is 4 and 1/9.

Since 4 and 1/9 is in lowest terms, this is our final answer.

So we can say that 1 and 4/9 + 2 and 6/9 is 4 and 1/9.

Answer:

1633.3 meters

Step-by-step explanation:

-Given the angle of depression is 31°, and the plane's height above the ground is 1400m.

-We use the Law of Sines to determine the distance between the plane and the rock.

-The angle of elevation from the rock to the plane is(corresponds to the plane's altitude):

[tex]\angle elevation=90-31\\=51\textdegree[/tex]

#Now, using Sine Law;

[tex]\frac{a}{Sin \A}=\frac{b}{Sin \ B}\\\\\\\frac{1400}{Sin \ 59}=\frac{d}{Sin \ 90}\\\\\\\\=1633.287\approx 1633.3\ m[/tex]

Hence, the direct distance between the plane and the rock is 1633.3 meters

Answer:

93

Step-by-step explanation:

Let's say President Reagan was x years old when he died. He was 69 years old at his first inauguration

(2*69)-x = 45

Wait. But how will we find x in that equation?

--> (2*69)-45 = x

That's better.

2*69 = 138

138-45 = 93

x=93

The rate of interest is 13%.

Step-by-step explanation:

Given,

Principal (P) = $560

Interest (I) = $145.60

Time (T) = 2 years

To find the rate of interest

Formula

If P principal was invested for T years at r% simple interest, the interest will be I = [tex]\frac{PTr}{100}[/tex]

So,

Putting the values of P, I, T we get,

145.60 =  [tex]\frac{560X2Xr}{100}[/tex]

or, r = [tex]\frac{145.60X100}{2X560}[/tex]

or, r = 13%

Hence,

The rate of interest is 13%.

Answer:

Sphere=48 beads

Cylinder=24 beads

Step-by-step explanation:

Let the number of cylinder beads be y and since she has twice as many sphere beads, the sphere beads will be 2y

The sum of sphere and cylinder beads will be y+2y=3y

This sum is equivalent to the total number given as 72

Therefore, equating 3y to be equal to 72 we obtain the equation

3y=72

Dividing by 3 on both sides we obtain that

Y=72/3=24 beads for cylinder

Since the sphere is 2y then 2*24=48

To confirm, it is evident that 48+24=72

Also, the number 48 is double/twice the number 24

Answer: The probability of being chosen by a wand made of holly or a wand made of dragon scale core is 0.4 or 40%

Step-by-step explanation: What we have are probabilities of two events. The first is the probability that Harry Potter is chosen by a wand made of Holly which is P(A). The other event is the probability that Harry is chosen by a wand with a dragon scale which is P(B).

In other to calculate P(A), there is a total of four possibilities, (that is holly, elm, maple and wenge). Therefore, the probability is derived as;

P(A) = Number of required outcomes/Number of all possible outcomes

P(A) = 1/4 or (0.25)

To calculate P(B), there is a total of five possibilities (that is phoenix feather, unicorn hair, dragon scale, raven feather and thestral tail). Therefore the probability is derived as;

P(B) = Number of required outcomes/Number of all possible outcomes

P(B) = 1/5 or (0.20)

However, the question requires the probability of P(A or B).

First we derive the probability of being chosen by a wand made of holly AND one made of a dragon scale core. In other words we shall calculate the probability of P(A and B) which is derived as;

P(A and B) = P(A) x P(B)

P(A and ) = 1/4 x 1/5

P(A and B) = 1/20 (0.05)

The probability of P(A or B) can now be calculated as follows;

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = (0.25 +0.20) - 0.05

P(A or B) = 0.45 - 0.05

P(A or B) = 0.40

Therefore the probability that Harry Potter is chosen by a wand made of Holly or a wand with Dragon scale core is 0.4 or 40%

Answer: P( A or B) = 2/5

Step-by-step explanation:

Answer:

-0.555

Step-by-step explanation:

The terminal point of the vector in this problem is

(-2,-3)

So, it is in the 3rd quadrant.

We want to find the angle [tex]\theta[/tex] that gives the direction of this vector.

We can write the components of the vector along the x- and y- direction as:

[tex]v_x = -2\\v_y = -3[/tex]

The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:

[tex]tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}[/tex]

However, since we are in the 3rd quadrant, the actual angle is:

[tex]\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}[/tex]

So now we can find the cosine of the angle, which will be negative:

[tex]cos \theta = cos(236.3^{\circ})=-0.555[/tex]

Answer:

well is a 50 50 chains that  Allen will get a red marble and

a 50 50 that the coin will land heads up.

Step-by-step explanation:

The position of the university marked x is shown in the attachment.

Given that university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital.

so we can say that the university position is gotten relative to the the position of the stadium and hospital.

The university is 50° from the stadium and then 350° from the hospital.

I.e it is N 50° E from the stadium and N 60° W from hospital.

The angle forms will be 50+60 = 110°

The point where the two lines intersect is the position of the university. Mark this point with a cross on the map.

Learn more about diagrams here;

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Total possible outcomes if a coin is flipped and a normal dice is rolled are   12

Probability of getting a tail and a five will be 1/12

The probability of getting a number less than five and a head  is 1/3

∴ Total possible outcomes  = (6 x 2) = 12

∴ Probability of getting a tail and a five will be 1/12

∴ The probability of getting a number less than five and a head =               (1/2)(4/6) = 4/12 = 1/3

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Answer:

A and C

Step-by-step explanation:

I did the assignment

Answer:

10 combinations

Step-by-step explanation:

What we have to do is calculate the number of combinations of 3 in 5.

The formula for the combinations is:

nCr = n!/r!(n-r)!

in this case n = 5 and r = 3

replacing

5C3 = 5!/3!(5-3)! = 5!/(3!*2!)

5C3 = 10

So there are 10 combinations in which Erika can enjoy the books on her trip

Answer:

The number of different combinations of 3 books that Erika can take on a trip if she has 5 books is 10

Step-by-step explanation:

Here we have the formula for combination given as follows;

[tex]\binom{n}{r} = \frac{n!}{r!(n-r)!}[/tex]

Where n is the number of set  elements = 5 and

r = Number of subset elements = 3

Therefore, plugging the values, we have;

[tex]\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{120}{6(2)} = 10[/tex]

Therefore, the number of different combinations of 3 books that Erika can take on a trip if she has 5 books = 10.

Answer:

s=-8

Step-by-step explanation:

Answer:

The decimal multiplier is 1.1663

Step-by-step explanation:

Since the increases are done successively we can find decimal numbers for each one and multiply both to have a single decimal representing the whole operation. When there's a increase this means that we have the original value (100%) summed by some other value, in this case 7%, so the new value would be 100% + 7% = 107%, we can transform this to a decimal number by dividing it by 100, so 107/100 = 1.07. The same applies to the 9% increase, so we would have 109/100 = 1.09. We can now multiply both to obtain a single decimal multiplier, we have:

1.07*1.09 = 1.1663

Answer:

Weight of large box = 18.5 Kg

Weight of small box = 13 Kg

Step-by-step explanation:

Let the weight of large box be X kg

Let the weight of small box be Y kg

So weight of 8 large boxes = 8X

weight of 3 small box be =  3Y

According to question

8 large boxes and 3 small boxes has a total weight of 187

mathematically it can be represented as

8X + 3 Y = 187

_________________________________________________

Second condition

weight of 2 large boxes = 2X

weight of 5 small box be =  5Y

According to question

2 large boxes and 5 small boxes has a total weight of 102 kilograms

mathematically it can be represented as

2X + 5Y = 102

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

we have two equation

8X + 3 Y = 187   -------------------A

2X + 5Y = 102   -------------------B

multiplying equation B with 4  on both side of equation we have

4*(2X + 5Y) = 4*102

=> 8X + 20Y = 408   -------------------C

Now subtracting equation A and C on both sides we have

8X + 3 Y - (8X + 20Y ) = 187 -408

8X - 8X + 3 Y -  20Y = -221

-17Y = -221

=> Y = -221/-17 = 13

Now substituting value of Y in equation B we have

2X + 5*13 = 102

=> 2X + 65 = 102

=> X = (102-65)/2  = 18.5

______________________________

Weight of large box = 18.5 Kg

Weight of small box = 13 Kg

The large box weighs 17 kg and the small box weighs 13 kg.

Let's denote the weight of a large box as x and the weight of a small box as y. We can set up a system of equations to solve for the weights:

8x + 3y = 187 (equation 1)

2x + 5y = 102 (equation 2)

To solve the system, we can multiply equation 1 by 2 and equation 2 by 8 to eliminate x:

16x + 6y = 374 (equation 3)

16x + 40y = 816 (equation 4)

Subtracting equation 3 from equation 4, we get:

34y = 442

Solving for y, we find y = 13.
Substituting this value back into one of the original equations, we find x = 17.

Therefore, the large box weighs 17 kilograms, and the small box weighs 13 kilograms.

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Answer:

-p - 30

Step-by-step explanation:

4p−5(p+6)

Distribute:

=4p+(−5)(p)+(−5)(6)

=4p+−5p+−30

Combine Like Terms

=4p+−5p+−30

=(4p+−5p)+(−30)

=−p+−30

=−p−30