what is the length of the hypotenuse?

Answer:

5 [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

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

3 [tex]\frac{2}{3}[/tex] = 11/3

In order to add fractions, the denominators, or the bottom numbers, have to be the same. To make them the same, find the common denominator (the lowest number that both the numbers can be divisible by)

8/5+ 11/3  the common denominator would be 15 so multiply the appropriate numbers to the denominators and the numerators (the top number)

24/15 + 55/15 = 79/15

Now simplify

79/15 = 5 [tex]\frac{4}{15}[/tex]

The no: of red marbles, that the bag contains if it has 24 purple marbles are 30 marbles.

a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its adjoint (in mathematics, linear algebra, mathematical study of a matrix or operator).

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

A unitary government is a type of government in which the whole government is controlled by a single entity, known as the central government. Actually, the center of authority for all administrative divisions and powers.

In the given question,

for every 4 purple marbles there are 5 red marbles

then for 1 purple marble there is 5/4 red marbles

again for 24 purple marbles, there are 30 red marbles

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Answer:

-3x+y=-5

Step-by-step explanation:

First, find the slope of the equation:

m=(y2-y1)/(x2-x1)  ==> m=slope of equation

(x1, y1), (x2, y2) ==> (x1=3, y1=4), (x2=2, y2=1)

m=(1-4)/(2-3)  ==> plugin x1=3, y1=4, x2=2, and y2=1

m=-3/(-1)

m=3

y=mx+b   ==> slope-intercept equation

1=3(2)+b ==> plugin 3 for m and (2, 1) where x=2 and y=1

1=6+b ==> solve for b

1-6=6-6+b

b=-5

y=3x+(-5)  ==> plugin -3 for m and -5 for b

y=3x-5 ==> simplify

Now, Isolate -5 since it is the only constant

y-3x=3x-3x-5  ==> isolate -5 by subtracting 3x on both sides

-3x+y=-5  ==> simplify and put in Ax+By=C form

y = 3x - 5

sorry can't help with step to step explanation......

By using algebra equation, the zeros of f(x)f(x) is ;

x = (-4 + 2i) and x = (-4 - 2i)

Given data :

This is a synthetic division shortcut. Write down the real root, then under a division symbol, the coefficients of the variables, 2, 18, 56, and 40. Drop down the 2 first, multiply by the root (-1) and add it to the next coefficient (18). 2*(-1) = -2, -2 + 18 = 16. Drop that one down. Next multiply 16 by the root, (-1) and add that to the next coefficient, 56 + (-16) = 40, drop down the 40, then lastly repeat this, multiply 40 by the root (-1) and add to the last coefficient 40 + (-40) = 0. If the remainder was not 0, then -1 would not have been a real root.

-1 | 2 18 56 40

......0 -2 -16 -40

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

......2 16 40 0

Put these into another equation, (2x2 + 16x + 40)

Factoring out a 2 we get 2(x2 + 8x + 20)

The factors of 20 are 2*10 and 4*5. 2+10 = 12, 4+5 = 9, so we must use the quadratic equation to find our roots.

-8 ± √(64 - 4(20))/2 = -4 ± √(-16)/2 = -4 ± 4i/2 = -4 ± 2i

So the other two roots are x = (-4 + 2i) and x = (-4 - 2i)

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1. The triangles are congruent based on the SSS congruence theorem.

2. The information is not enough.

3. Both are congruent by the HL congruence theorem.

If two triangles have a pair of congruent hypotenuses and a pair of congruent legs, then both triangles ae congruent to each other based on the HL congruence theorem.

The SSS Congruence Theorem states that if any two triangles have three pairs of corresponding sides that are congruent to each other, then the triangles are congruent.

1. Based on the SSS congruence theorem, the pair of angles in figure 1 are congruent.

2. There is no information available that shows the triangles have a pair of congruent hypotenuses, nor have three pairs of corresponding congruent sides. Th information given is not enough to prove that they are congruent by SSS or HL.

3. Based on the HL congruence theorem,, they are congruent to each other.

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The weight of an object is the amount of the gravitation pull of the Earth on the object. No, the weight of a bike is not a function of its age.

The mass of an object is the quantity of matter it contains, while the weight is the amount of gravitational pull of the Earth on the object. Thus the greater the mass of an object is, the greater its weight. This implies that the weight of an object can be influenced by its value of mass.

The mass of an object can be determined or measured by the use of any of the weighing balances, while the weight of an object can be measured by the use of any of the spring balances. Therefore, the answer to the given question is NO. The weight of a bike is NOT a function of its age. The weight of the bike will depend on the number, and weight of its component parts.

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Answer:

[tex]tn = {3 \times \sqrt{2} }^{n - 1} [/tex]

Step-by-step explanation:

since it is geometric sequence we will use the formula

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

n = 10

r = √2

a = 3

lets first see the result of the 10th term

[tex]t10 = {ar}^{10 - 1} [/tex]

[tex]t10 = {ar}^{9} [/tex]

[tex]t10 = {3 \times \sqrt{2} }^{9} [/tex]

t10 = 3 × 22.63

t10 = 67.89

approximately 68

t10 = 68

for the nth term

Tn = ar^n–1

[tex]tn = {3 \times (\sqrt{2} })^{n - 1} [/tex]

i hope this helps

Answer:

[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]

[tex]a_{10}=48 \sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the given values of a and r into the formula to create an equation for the nth term:

[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]

To find the 10th term, substitute n = 10 into the equation:

[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{10-1}[/tex]

[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{9}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{\frac{9}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{4+\frac{1}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{4} \cdot 2^{\frac{1}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 16 \cdot \sqrt{2}[/tex]

[tex]\implies a_{10}=48 \sqrt{2}[/tex]

Since, F value is =19.056 is greater than F critical value =3.3541

Therefore, We have enough evidence that null hypothesis is not rejected

A hypothesis is a theory that is put up to account for a phenomenon. Unless it can be tested through the scientific method, a hypothesis cannot be referred to as a scientific hypothesis. Scientific theories frequently begin with historical observations that cannot currently be fully explained by existing knowledge.

Here,

Null hypothesis,

[tex]H_{0}[/tex]: u1 = u2 =u3

u1,u2,u3 are means of stress  scale for group 1 , group 2 and group 3

Alternate hypothesis,

[tex]H_{A}[/tex] : u1≠u2

The F value is =19.056

Using F critical value α=0.05

df numerator =2 , df denominator = 27

F critical value =3.3541

Conclusion : F value is =19.056 is greater than F critical value =3.3541

Therefore, We have enough evidence that null hypothesis is not rejected

We, conclude that all three groups are equals in terms of mean.

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Answer: X= -1± √(-1)² - 4(7)(9)

2(7)

Step-by-step explanation: The correct equation for using the quadratic formula to solve 7x² = 9 + x for x is:

X= -1± √(-1)² - 4(7)(9)

2(7)

The quadratic formula is given by the equation X = -b ± √(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, we have a = 7, b = 1, and c = 9, so plugging these values into the formula gives us the equation above.

The equation used to solve Quadratic Equation is -1 ± [√((-1)² - 4(7)(-9])/2(7)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

we have the Quadratic Equation as:

7x² = 9+ x

7x² -x -9= 0

Using Discriminant method

x = -b ± √(b² -4ac)/2a

x = 1 ± √(1² - 4(7)(-9)/2(7)

x = 1 ± √(1 + 196)/14

Thus, the formula used 1 ± [√(1² - 4(7)(-9])/2(7)

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Answer:

y = x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = 1 , then

y = x + c ← is the partial equation

to find c substitute (2, 3 ) into the partial equation

3 = 2 + c ⇒ c = 3 - 2 = 1

y = x + 1 ← equation of line

Since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles.

To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles.

At α = 0.05, test the shipping firm's claim.

Under H0: μ 200  Vs H1: > 200  (Right tailed test)

n = 16, x bar = 205 , s = 14

Null Hypothesis;  H0:  μ = 35000  Vs  H1: < 35000

(Mean life of brand of tire less than 35000 miles).

Under H0 test statistic is

t = (x bar - μ) / (s / √n) ≈ [tex]t_n_-_1[/tex]

Now, n = 18, x bar = 34,200,  s = 12000

t = (34000 - 35000) / (1200 / √18) = -2.8284

t - critical value of α = 0.05 for left tailed at (18 - 1) df = -2.11

Therefore t calculated (= -2.8284) < -2.11

So, we do not reject H0.

Hence, since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.

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Answer:

5.85369.421.5 does not have a quotient because it is not a mathematical expression.

40.42 ÷ 4.3 = 9.4

15.48 ÷ 0.72 = 21.4

86.4 ÷ 2.4 = 36.0

50.31 ÷ 8.6 = 5.84

To test the claim that the two samples described come from populations with the same mean, we can use a two-sample t-test.

(a) The degree of freedom is 27

(b) The test statistic is -2.67

(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0 : we do not reject the null hypothesis.

(d) |t| > 2.70

(1) The degree of freedom for the two-sample t-test is calculated as

(2) The test statistic for the two-sample t-test is calculated as:

Plugging in the values, we get:

(3) To determine the rejection region for the test, we can use a significance level of α = 0.01. For a two-tailed test with α = 0.01, the critical value for t is approximately 2.70. Since our test statistic (-2.67) is less than the critical value, we do not reject the null hypothesis.

(4) For the rejection region, we need to consider values of t that are either greater than or less than the critical value. Therefore, we need to consider |t| values that are greater than 2.70. |t| > 2.70.

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Using proportions, the value of 3500 Yen on October 8, 1982 is 13.1 USD

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

On October 8, 1982;

267.38 Yen = 1US

The cost of 3500 Yen = ?

267.38 Yen = 1 USD

35000 Yen = x USD

Cross multiply both sides and solve for x

x * 267.38 = 3500 * 1

267.38x = 3500

Divide both sides by coefficient of x

267.38x / 267.38 = 3500 / 267.38

x = 13.1

The value of 3500 Yen is 13.1 USD

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Answer: 8,000

Step-by-step explanation: So, to find how to round this to the nearest 1000, we need to look at the 3 digits being the 7. So, 899 is greater than 500, so we round up, so 7 + 1 is 8, and we change those 3 digits behind the zero to 0's, so we get 8,000. I hoped this helped.

Answer:

8000

7899 rounded to nearest thousand is 8000, because 7 is in thousand's place value, and the number after that is 8, which is more than 5, so 1 is added to 7, and it becomes 8. The rest of the numbers turn to 0.

so you get 8000.

hope it helps :)

The measure of an angle m ∠YBA=47°.

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

Since,

ΔFBA=ΔYBA

The two triangles in the provided illustration are comparable.

So,

From the figure:

m ∠FBA=47°

So, m ∠YBA=47°

Therefore, the measure of angle  m ∠YBA=47°

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The correct statement that assigns a random integer between 1 and 10, inclusive, to rn is (D).

int rn = (int) (Math.random() * 10) + 1.

The method Math.random() generates a random number between 0 and 1, inclusive. If we multiply this number by 10, we will get a random number between 0 and 10, exclusive. If we then add 1 to this number, we will get a random number between 1 and 11, exclusive. If we then take the integer part of this number using the (int) cast, we will get a random integer between 1 and 10, inclusive. This is exactly what statement (D) does.

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Answer:No

Step-by-step explanation:

0+3 = 3, not zero

Answer:

the data item that corresponds to z = -3 is 80.

Step-by-step explanation:

From the linear function, the rate of change is 35 and the unit cost is 35

A linear function is defined as a function that has either one or two variables without exponents.

In this problem, we have to write a linear function that models the table given. This will take the form of y = mx + c

m = slope or rate of change and c = constant or unit cost of the product.

The formula of slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

Taking two points from the table;

m = 215 - 180 / 5 - 4

m = 35

Using the slope of the line, we can find the y - intercept of the function.

y = mx + c

215 = 35(5) + c

215 = 175 + c

c = 215 - 175

c = 40

The linear function of the table is y = 35x + 40

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Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.

We follow these steps in order to arrive at the answer:

Let the amount invested in bonds be x

Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.

The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x

The interest earned on bonds will be 0.06x0.06x

The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x

The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x

The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.

Hence total interest is:

1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x

Simplifying we get,

1000 -400 = 0.1x1000−400=0.1x

600 = 0.1x600=0.1x

\mathbf{x = 6,000}x=6,000

Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000

Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000

Answer:

D.

Step-by-step explanation:

Thousandhts

Answer:

d. 7 thousandths

WHY?

0.007 places is a decimal representation of a number. In the decimal system, the value of a digit is determined by its position relative to the decimal point. In this case, the number 0.007 has three digits to the right of the decimal point, so it is said to have three decimal places. The value of each digit in this number is determined by its position: the first digit (0) is in the hundredths place, the second digit (0) is in the thousandths place, and the third digit (7) is in the ten-thousandths place.

This question doesn't seem completed to me. Is there anything more after this?

Answer:

11 inches

Step-by-step explanation:

If one inch represents 210 feet, then divide 2310 by 210 to get the number of inches in the scale drawing.

Answer:

11 inches

Step-by-step explanation:

2310/210 = 11

Answer:

y = -37

Step-by-step explanation:

y = -5 - 8x

y = -5 - 8(4)

y = -5 + ( - 8 x 4 )

y = -5 + ( - 32)

y = -37

Answer:

$2.75

Step-by-step explanation:

The difference in cost for 33 articles and 30 articles is

$57.40 - $49.15 = $8.25

From 30 to 33 articles, the difference is 3 articles.

3 articles cost $8.25.

Cost per article = $8.25/3 = $2.75

Answer: 5/8

Step-by-step explanation: There are 8 members. Out of 8, there are 5 people's weight that are higher than 135. Therefore the answer is 5/8.

There are 9.75 servings, not 13 servings.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the number of 3/4 pound servings in pounds of turkey

she calculates that there are 13 servings.

so,

9 (3/4) = (36 + 3) /4

= 39/4

= 9.75

Hence, there are 9.75 servings, not 13 servings.

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A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. The lateral line receptors are most likely is Mechanoreceptors.

Given that,

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it.

We have to find according to your understanding of sensory receptors, the lateral line receptors are most likely is.

We know that,

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. According to your understanding of sensory receptors, the lateral line receptors are most likely is Mechanoreceptors.

Mechanoreceptors, also known as Mechanoreceptors, are specialized neurons that react to pressure and deformation caused by mechanical forces. They are surrounded by sensory neurons, which translate external pressure into electrical signals that are sent to the brain.

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