Solve the equation for y.
3x + 7y= 29

The answer to the sum is: ∑ k⁴ (k  ranges from 1 to 6)

Express the sum in sigma notation :

According to the question,

1 = lower limit of summation

k = the index of summation

1 + 16 + 81 + 256 + 625 + 1296 = 1² + 4² + 9² + 16² + 25² + 36²

                                                 = 1⁴ + 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ ( i.e 16 = 4²=(2²)²)

                                                 = ∑ k⁴ (k ranges from 1 to 6)

 So, The answer to the sum is - ∑ k⁴ (k ranges from 1 to 6).    

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Answer:

I think it's all the options but I cant confirm.

Step-by-step explanation:

adjacent angles are angles that:

- have the same vertex

- share one side

Answer:

3(x+4)

Step-by-step explanation:

unknown number = x

sum of a number and 4 = (x+4)

then the sum is multiplied by 3 so

3(x+4)

Also can be distributed out

3(x) + 3(4)

3x+12

Answer:

19.50/6=c c=3.25

Step-by-step explanation:

In this case C=3.25

Answer:

19.50÷6= c

Step-by-step explanation:

19.50÷6 =c

divide to find how much 1 cup of coffee is

As per the intersecting point, the length of AC is 4x + 10.

The diagonals of a rectangle are two lines that intersect at the midpoint of the rectangle. In this case, the diagonals of rectangle ABCD intersect at point E.

If AE = 2x + 5 and BD = 5x + 2, then we can calculate the length of AC. We know that AC is the sum of AE and ED, so AC = AE + ED.

Since the diagonals of a rectangle intersect at the midpoint of the rectangle, AE and ED are equal. Therefore, AC = 2x + 5 + (2x + 5) = 4x + 10.

Therefore, the length of AC is 4x + 10. Knowing the lengths of the diagonals can help us find the length of the sides of the rectangle, and can also be useful in finding the area of the rectangle

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In order to find the length of T, take into account the law of sines, given by:

u/(sin

Morever, consider that the sum of the interior angles of a triangle is equal to 180°:

next, use the equation u/(sinsolve for t and replace the values of the rest of parameters, as follow:

t = [u/(sin

t = [40 in/(sin36°)](sin71°)

t = 64.34 in ≈ 64 in

Hence, the value of t is 64 in

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

1.7

Step-by-step explanation:

25.5 divided by 15

The statistical analysis of the data using a two-sample t-test indicates;

(a) B. Yes, the Meters On data appears to have higher speeds

A. No, there does not appear to be any outlier

(b) H₀; \(\mu_{on}\) = \(\mu_{off}\)

H₁; \(\mu_{on}\) > \(\mu_{off}\)

The P-value for the test is about 0.037

A two-sample t-test is used to determine if there is a difference between the means of two independent groups of data.

(a) The average of the data values are;

Ramp meters on;

\(\mu_{on}\) = (29+47+55+38+32+25+42+47+51+36+55+41+43+25+47)/15 ≈ 40.87

\(\mu_{off}\) = (25+25+43+35+36+31+48+37+19+29+22+40+36+50+40)/15 ≈ 34.4

The higher average value for the speed with the Ramp meters on indicates;

B. Yes, the Meters On data appears to have higher speeds

The five number summary are;

Ramp Meters On

Min = 25, Max = 55, Q₁ = 32, Q₂ = 42, Q₃ = 47

IQR = 47 - 32 = 15

Outlier = 47 + 1.5 × 15 = 69.5

32 - 1.5 × 15 = 9.5

Therefore, there are no outliers for the Ramp Meters On

Ramp Meters Off

Min = 19, Max = 50, Q₁ = 25, Q₂ = 36, Q₃ = 40

IQR = 40 - 25 = 15

Outlier = 40 + 1.5 × 15 = 62.5

25 - 1.5 × 15 = 2.5

Therefore, there are no outliers for the Ramp Meters Off data

(b) The null hypothesis is; H₀; \(\mu_{on}\) = \(\mu_{off}\)

The alternative hypothesis is; H₁; \(\mu_{on}\) > \(\mu_{off}\)

(c) The two sample t-test, can be obtained using the formula;

\(t_{cal} = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} ) } }\)

Where; \(\bar{x}_1\) = 40.87

\(\bar{x}_2\) = 34.40

s₁ = 9.91

s₂ = 9.20

n₁ = n₂ = 15

Therefore; \(t_{cal}\) = 1.8516. The degrees of 15 + 15 - 2 = 28, and the one-tailed hypothesis, indicates, using an online tool;

The p-value is less than 0.05, therefore, the result is significant.

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Refer to the attachment.

\(\huge\text{Hey there!}\)

\(\large\textsf{c - 8y}\\\large\text{= -4 - 8(-5)}\\\large\text{= -4 - (-40)}\\\large\text{= -4 + 40}\\\large\text{= 36}\\\\\large\boxed{\text{Therefore, your answer: 36}}\huge\checkmark\\\\\large\text{Good luck on your assignment \& enjoy your day!}\\\\\frak{Amphitrite1040:)}\)

Answer:

she gave away 6 cupcakes

Step-by-step explanation:

3/7 is the same as 6/14.

if she gave away 6/14 cupcakes, she gave away 6 cupcakes

Answer:

The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.

Hope this helps

Step-by-step explanation:

The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.

Hope this helps

Option A. The statement that can be said to be true for h is h(2) = 16

If we look at the domain and range, we can rule out some straight away.

For h - 3 = -1

this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25

When h is 13 = 18

This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11

When h is 8 = 21

there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19

Therefore on h(2) = 16

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The tank holds approximately 994,040 liters.

The volume of a right circular cylinder is given by the formula:

V = πr^2h

Where

The cylinder's diameter is specified as 13 m, hence the radius may be computed using the formula: r = d/2 = 13/2 = 6.5 m

The cylinder is described as having a 6 m length.

These values are substituted into the volume calculation to produce the following result:

V = π(6.5)^2(6)

V ≈ 994.04 cubic meters

Since 1 cubic meter equals 1000 liters, we can convert the volume to liters by multiplying by 1000.

V = 994.04 cubic meters x 1000 liters/cubic meter

V = 994,040 liters

Therefore, the tank holds approximately 994,040 liters.

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Answer:

7. No

8. $6.11

Step-by-step explanation:

7. 180 / 3 = 60  350 / 5 = 70

8. 20 / 2 = 10  12.22 / 2 = 6.11

Step-by-step explanation:

for 7:

they're not equivalent

20 batteries 12.22$

10 batteries 6.11 $

Answer:

\(y=1-Ae^{\frac{1}{2}x^2-x}\)

Step-by-step explanation:

Given equation:

\(\dfrac{\text{d}y}{\text{d}x}=(1-x)(1-y)\)

Separate the variables by moving all the y terms to one side of the equation and all the x terms to the other side:

\(\implies \dfrac{1}{(1-y)}\;\text{d}y=(1-x)\;\text{d}x\)

Integrate both sides of the equation separately:

\(\implies \displaystyle \int \dfrac{1}{(1-y)}\;\text{d}y= \int (1-x)\;\text{d}x\)

\(\implies -\ln |1-y|+C=x-\dfrac{1}{2}x^2+D\)

\(\implies \ln |1-y|-C=\dfrac{1}{2}x^2-x-D\)

Write the two constants as one (a = -D + C):

\(\implies \ln |1-y|=\dfrac{1}{2}x^2-x+a\)

Take exponents of both sides:

\(\implies e^{\ln |1-y|}=e^{\frac{1}{2}x^2-x++a}\)

\(\textsf{As }\; e^{\ln y}=y:\)

\(\implies 1-y=e^{\frac{1}{2}x^2-x+a}\)

\(\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:\)

\(\implies 1-y=e^{\frac{1}{2}x^2-x}e^{a}\)

As \(e^{a}\) is just a constant, replace it with A:

\(\implies 1-y=Ae^{\frac{1}{2}x^2-x}\)

Rearrange to make y the subject:

\(\implies y=1-Ae^{\frac{1}{2}x^2-x}\)

Answer:

AB = 11

Step-by-step explanation:

Using the external secant property,

CB*CA = CD*CL (=CT^2  if T is tangent throught C)

substitute values,

7*(7+2x+3) = 9*(9+x+1)

Expand and simplify

70+14x = 90 + 9x

5x = 20

x = 4

=>

AB = 2x+3 = 2(4)+3 = 8+2 = 11

Answer:

we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.

Step-by-step explanation:

We can use the commutative property of multiplication to see that 3 x 4 is the same as 4 x 3 and 6 x 2 is the same as 2 x 6. When multiplying two numbers, the order of the numbers does not affect the product. Therefore, we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.

NEED MORE EXPLANATION?

The commutative property of multiplication states that when multiplying two numbers, the order of the numbers does not affect the product. This means that 3 x 4 is the same as 4 x 3, and 6 x 2 is the same as 2 x 6. We can use this property to compare 4 x 3 and 2 x 6, equal to 12. Therefore, we can see that both products are identical and neither is greater.

Answer:

Triangle

Step-by-step explanation:

It has three side unlike the others can't have three sides

The fraction of those who were delivered by car will be 1/6.

It should be noted that from the information given, the students were questioned on how they got to schoo and half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.

Therefore, the fraction of those who were delivered by car will be:

= 1 - (1/2 + 1/3)

= 1/2 - 5/6

= 1/6

In conclusion, the fraction of those who were delivered by car will be 1/6.

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Answer:

412.92

Step-by-step explanation:

\(A = P(1+\frac{r}{n} )^{nt}\)

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)

Answer:

-4

Step-by-step explanation:

parenthesis : -1

exponent : 4

multiplication : -4

done!

i hope that made sense, but if you need help, im here!

A dilation is a function from a metric space into itself that satisfies the identity for all points, where is the distance from to and is some positive real number. In Euclidean space, such a dilation is a similarity of the space. Dilations  always  change the size but not the shape of  object or figure.

Answer: Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Hope this helped!

Sending U good luck!

Answer:

B. 533in²

Step-by-step explanation:

Step 1: Find the area of the rectangle

A = lw

A = (29)13

A = 377

Step 2: Find the leg of the triangle

13 + 11 = 24

Step 3: Find the area of the triangle

A = 1/2bh

A = 1/2(24)(13)

A = 12(13)

A = 156

Step 3: Add the areas of the 2 figures together

377 + 156 = 533

Answer:

\( \frac{41}{3} \times 3 \times \frac{62}{3} = \frac{806}{3} = 268 \)

Answer:

D.

Step-by-step explanation:

Step 1: Write slope-intercept form

y = mx + b

Step 2: Solve for m

The probability that each bill is a $1 bill is given as follows:

1/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The bills are replaced, hence we consider that for each trial, there is a 1/4 probability of selecting a $1 bill, as one out of the four bills are of $1.

Hence the probability that each bill is a $1 bill is obtained as follows:

p = 1/4 x 1/4

p = 1/16.

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Answer:

14.3 ft

Explanation:

We can represent the situation as:

Now, we can relate the measure of the angle, the height x, and the distance 10 ft using the trigonometric function tangent as:

So, solving for x, we get:

Therefore, the height of the nest to the nearest tenth is 14.3 ft.

Answer:

New moon

Step-by-step explanation:

Answer:

c-new moon

Step-by-step explanation: