Kate used 555 grams of wool to knit a sweater, a hat, and a scarf. She used 5 times fewer grams for the hat than for the sweater. She used 5 grams more for the hat than for the scarf. How many grams of wool did she use to knit each item?

Answer:

3/5

Step-by-step explanation:

The word "Restaurant" contains a total of 10 letters, out of which 4 of the letters are vowels and 6 of the letters are consonants. The probability of selecting a vowel out of this word is:

P(selected letter is a vowel) = number of vowels/number of letters.

P(selected letter is a vowel) = 4/10 = 2/5.

Similarly, probability of selecting a non-vowel out of this word is:

P(selected letter is not a vowel) = number of non-vowels/number of letters.

P(selected letter is not a vowel) = 6/10 = 3/5.

Given that one of the letters randomly falls down, and assuming that the probabilities of each letter falling down is uniform and independent from each other, then:

P(a non-vowel falls down) = non-vowels/total = 6/10 = 3/5.

So the correct answer is 3/5!!!

Answer:

6

Step-by-step explanation:

60% of 40 = 24

25% of 24 = 6

Therefore, 6 girls in  the class wear glasses.

Answer:

So we have

[tex](fg)(x)=3x^3+x^2-18x-6[/tex]

[tex](f \circ g)(x)=3x^2-17[/tex]

Step-by-step explanation:

I'm going to do two problems just in case.

We are given [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex].

[tex](fg)(x)=f(x)g(x)=(3x+1)(x^2-6)[/tex]

Multiply out using foil!

First:  3x(x^2)=3x^3

Outer: 3x(-6)=-18x

Inner: 1(x^2)=x^2

Last: 1(-6)=-6

-------------------Add together:

[tex]3x^3+x^2-18x-6[/tex]

[tex](f \circ g)(x)=f(g(x))=f(x^2-6)=3(x^2-6)+1=3x^2-18+1=3x^2-17[/tex]

Answer:

b

Step-by-step explanation:

I would use b.

Why?

[tex]2 \csc(2x)[/tex]

[tex]2 \frac{1}{\sin(2x)}[/tex]

[tex]\frac{2}{\sin(2x)}[/tex]

[tex]\frac{2}{2\sin(x)\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)\cos(x)}{/tex]

[tex]\frac{1}{\sin(x)\frac{1}{\cos(x)}[/tex]

[tex]\csc(x) \sec(x)[/tex]

I applied the identity sin(2x)=2sin(x)cos(x) in line 3 to 4.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember these identities:

[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]

Knowing this, we can say that:

[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]

Now we need to use the following Double angle identity :

[tex]sin(2x)=2sin(x)cos(x)[/tex]

And solve for [tex]sin(x)cos(x)[/tex]:

[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]

The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:

[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]

Answer:

-3 , 21

Step-by-step explanation:

RS = R + S = 12

S lies on 9

There are 12 spaces in between R & S, so you can add and subtract 12 from S:

9 - 12 = -3

9 + 12 = 21

R can be located on either -3 or 21.

~

ANSWER

(0, 1), (1, 3), (2, 9), (3, 27)

EXPLANATION

The first and third options are completely out because the y-value of an exponential function is never zero.

For the second option the y-values has no geometric pattern or common ratio.

For the last option, we can observe the following pattern

[tex]1 = {3}^{0} [/tex]

[tex] {3}^{1} = 3[/tex]

[tex] {3}^{2} = 9[/tex]

[tex] {3}^{3} = 27[/tex]

:

:

[tex] {3}^{x} = y [/tex]

The correct choice is the last option

Answer:

D

Step-by-step explanation:

Answer:

1/12 of a gallon of water in each container

Step-by-step explanation:

Answer = [tex]\frac{Water}{Containers}[/tex] = 1/12

Answer:

Oliver poured [tex]\frac{1}{12}[/tex] gallons of water in each container.

Step-by-step explanation:

Oliver has the amount of water = 0.5 gallons.

He pours all of the water into 6 containers.

So amount of water in each container will be = [tex]\frac{\text{Total amount of water}}{\text{Number of containers}}[/tex]

= [tex]\frac{0.5}{6}[/tex]

= [tex]\frac{\frac{1}{2} }{6}[/tex]

= [tex]\frac{1}{12}[/tex] gallons of water.

Therefore, in each container amount of water poured will be [tex]\frac{1}{12}[/tex] gallons.

Answer:

$225,000

Step-by-step explanation:

To calculate the percentage change we will apply the formula:

p= N-O/O *100

p is the increased percentage

N is the current value

O is the old value.

Substitute the values in the formula:

36 = 306,000 - O/O *100

Divide both the sides by 100

36/100 = 306,000 - O/O *100/100

36/100 = 306,000 - O/O

Now multiply O at both sides

36/100 * O = 306,000-O/O * O

At R.H.S O will be cancelled by O

At L.H.S 36/ 100 = 0.36

0.36 O= 306,000-O

Combine the like terms:

0.36 O+O =306,000

1.36 O = 306,000

Divide both the terms by 1.36

1.36 O/ 1.36 = 306,000/1.36

O= $225,000

Therefore  when the house was purchased its value was $225,000....

Answer:

Step-by-step explanation:

Put a = -0.1 to the first an second equation and find velue of b:

3 = 10a + b

3 = 10(-0.1) + b

3 = -1 + b             add 1 to both sides

4 = b → b = 4

2 = 20a + b

2 = 20(-0.1) + b

2 = -2 + b       add 2 to both sides

4 = b → b = 4

CORRECT

Answer:

x = 1 - t and y = -2.5 - 2.5t.

Step-by-step explanation:

Parametric equations are the equations in which the all the variables of the equation are written in terms of a single variable. For example in 2-D plane, the equation of the line is given by y=mx+c, there x is the independent variable, y is the dependent variable, m is the slope, and c is the y-intercept. The equation of the given line is 10x - 4y = 20. The goal is to convert the variables x and y in terms of a single variable t. First of all, take two points which lie on the line. By taking x=1, y comes out to be -2.5 and by taking x=0, y comes out to be -5. The general form of the straight line is given by:

(x, y) = (x0, y0) + t(x1-x0, y1-y0), where (x, y) is the general point, (x0, y0) is the fixed point, t is the parametric variable, and (x1-x0, y1-y0) is the slope.

Let (x0, y0) = (1, -2.5) and (x1, y1) = (0, -5). Substituting in the general equation gives:

(x, y) = (1, -2.5) + t(-1, -2.5). This implies that x = 1 - t and y = -2.5 - 2.5t!!!

Answer:

C. x=2t, y=5t-5

Step-by-step explanation:

Answer:

False.

Step-by-step explanation:

To see if these sides can form a right triangle, all we need to do is see if the following equation holds [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the larger measurement.  [tex]a \text{ and } b[/tex] it doesn't really matter which you assign as 5 or 8.

So I'm choosing the following [tex]a=5,b=8,c=12[/tex].

[tex]c[/tex] has to be 12 because 12 is the largest.

Now we got to see if [tex]a^2+b^2=c^2[/tex] holds.

That is, we need to see if [tex]5^2+8^2=12^2[/tex] holds.

[tex]5^2+8^2=12^2[/tex]

[tex]25+64=144[/tex]

[tex]89=144[/tex]

That's totally false.  89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.

1st one

Step-by-step explanation:

I have answered ur question

Answer:

A

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex]

Solution set is (4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex] )

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

[tex](x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0[/tex]

Therefore, the general form of the equation of circle given is:

[tex]x^2+y^2-6x-16y+48=0[/tex]

Hence, option A is correct ..

Answer:

D

Step-by-step explanation:

Given

9 - 7x = (4x - 3)² + 5 ← expand the squared factor

9 - 7x = 16x² - 24x + 9 + 5, that is

9 - 7x = 16x² - 24x + 14 ( subtract 9 - 7x from both sides )

0 = 16x² - 17x + 5, that is

16x² - 17x + 5 = 0 ← in standard form → D

To find the exact value of tan^-1(-sqrt(3)), we first rewrite the equation using the definition of the arctangent function. Next, we use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the equation and solve for sin(x). We find that sin(x) = sqrt(3)/2. By looking at the unit circle, we determine that the angle whose sine is sqrt(3)/2 is pi/3 radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.

To find the exact value of tan^-1(-sqrt(3)), we need to recall the definition of the arctangent function. The arctangent function returns an angle whose tangent is equal to a given number. In this case, we are looking for an angle whose tangent is -sqrt(3). Since tan(x) = sin(x)/cos(x), we can rewrite the equation as -sqrt(3) = sin(x)/cos(x).

Next, we can use the fact that sin^2(x) + cos^2(x) = 1 to rewrite the equation as -sqrt(3) = sin(x)/sqrt(1 - sin^2(x)). Cross-multiplying and rearranging, we get -sqrt(3)*sqrt(1 - sin^2(x)) = sin(x).

Now, we can square both sides and simplify the equation to get -3*(1 - sin^2(x)) = sin^2(x). Expanding and rearranging, we have -3 + 3sin^2(x) = sin^2(x). Combining like terms and isolating sin^2(x), we get sin^2(x) = 3/4. Taking the square root of both sides, we find sin(x) = sqrt(3)/2.

Finally, we can find the angle whose sine is sqrt(3)/2 by looking at the unit circle. The angle is pi/3 in radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.

https://brainly.com/question/33989272

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This is a linear equation in standard form [tex]\( Ax + By = C \).[/tex] None of the options provided in the multiple-choice question exactly match this equation in standard form

To find the equation of a line perpendicular to the given line and passing through a specific point, follow these steps:

1. Identify the slope of the original line.

  The line given is [tex]\( y = -10x + 1 \)[/tex]. The slope (m) of this line is -10.

2. Find the perpendicular slope:

  The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the perpendicular slope [tex]\( m_{\perp} \) is \( \frac{1}{10} \)[/tex]  because [tex]\( m_{\perp} = -\frac{1}{m} \).[/tex]

3. Use the point-slope form to find the equation:

  The point-slope form is [tex]\( y - y_1 = m_{\perp}(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is the point the line passes through, which is (5,7) in this case.

4. Plug in the point and the perpendicular slope:

  [tex]\( y - 7 = \frac{1}{10}(x - 5) \)[/tex].

5. Simplify the equation to get it into slope-intercept form  [tex](\( y = mx + b \))[/tex]:

  [tex]\( y = \frac{1}{10}x - \frac{1}{10}(5) + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x - \frac{1}{2} + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x + \frac{13}{2} \)[/tex] after combining like terms.

The equation in slope-intercept form is [tex]\( y = \frac{1}{10}x + \frac{13}{2} \),[/tex]which corresponds to one of the choices given in the multiple-choice question. Let's identify which one it is.

The equation that represents a line which is perpendicular to the line [tex]\( y = -10x + 1 \)[/tex] , passing through the point (5,7), is:

[tex]\[ y = \frac{1}{10}x + \frac{13}{2} \][/tex]

This can be simplified to:

[tex]\[ 10y = x + 65 \][/tex]

Or:

[tex]\[ x - 10y = -65 \][/tex]

This is a linear equation in standard form \( Ax + By = C \). None of the options provided in the multiple-choice question exactly match this equation in standard form

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

* Lets explain how to solve the question

- The graph represents the relation between the number of months

  since the business opened and the total amount of money the

  business has earned

- The x-axis represents the number of month

- The y-axis represents the amount of money

- In the line the slopes from any two points on the line are equal

- The slope of the line whose end-points are (x1 , y1) and (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- The equation of the line is y = mx + c ,where m is the slope of the line

 and c is the y-intercept

* Lets check is the relation between x and y is linear by calculating the

 slopes between each to points

∵ (2 , 1990) , (5 , 4225) , (9 , 7205) are points from the graph

- m1 is the slope of the points (2 , 1990) and (5 , 4225) , m2 is the slope

 of the points (5 , 42250) and (9 , 7205) , m3 is the slope of the points

 (2 , 1990) and (9 , 7205)

∵ [tex]m_{1}=\frac{4225-1990}{5-2}=745[/tex]

∵ [tex]m_{2}=\frac{7205-4225}{9-5}=745[/tex]

∵ [tex]m_{3=\frac{7205-1990}{9-2}}=745[/tex]

∴ m1 = m2 = m3 = 745

∴ The relation between the number of months and the amount of

   money is linear

* The slope is 745

∵ The form of the linear equation is y = mx + c

∵ m = 745

∴ y = 745 x + c

- The y-intercept means the line intersect the y-axis at point (0 , c),

  then to find c substitute x and y of the equation by the coordinates

  of any point on the line

∵ x = 2 , y = 1990

∴ 1990 = 745(2) + c

∴ 1990 = 1490 + c ⇒ subtract 1490 from both sides

∴ c = 500

∵ c is the y-intercept

* The y-intercept is 500

* The slope represents the rate of increasing of money per month

∴ The amount of money increases by $745 per month

* The y-intercept represents the initial amount of money when the

  business opened

∴ The business opened with initial amount $500

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

Answer:

nope its not. You should  count it like this  (8 / 2) * (2 + 2)

Step-by-step explanation:

(8 / 2) * (2 + 2)

4 * 4

16

[tex]\text{Hey there!}[/tex]

[tex]\text{PEMDAS means: Parentheses, Exponents, Multiplication, Division, Addition}\\\text{, \& Subtraction}[/tex]

[tex]\text{\underline{No}, it is \underline{NOT} correct because you had to work with the parentheses first}[/tex]

[tex]\dfrac{8}{2}(2 + 2) = \ ? \\ \\ (2 + 2) = 4 \\ \\ \dfrac{8}{2}(4) = \ ? \\ \\ \dfrac{8}{2}= 4 \\ \\ \text{4(4)\ = 16} \\ \\ \boxed{\boxed{\huge\text{Answer should be: 16 }}}[/tex]

[tex]\text{You had to do what was inside the parentheses first, then}\text{ divsion}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

6^ -24

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

(6^-4)^6  = 6^ (-4*6) = 6^ -24

Answer:

The distance is equal to [tex]3\sqrt{13}\ units[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]R(-1,0)\\S(8,6)[/tex]  

substitute the values

[tex]d=\sqrt{(6-0)^{2}+(8+1)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(9)^{2}}[/tex]

[tex]d=\sqrt{36+81}[/tex]

[tex]d=\sqrt{117}\ units[/tex]

Simplify

[tex]d=3\sqrt{13}\ units[/tex]

Answer:

Step-by-step explanation:

2(9+4)

According to the BODMAS rule:

B = BRACKET

O = OPEN

D= DIVISION

M = MULTIPLICATION

A = ADDITION

S= SUBTRACTION

First we will solve the bracket:

=2(9+4)

=2(13)

=26....

Answer:

A, B, and C

Step-by-step explanation:

= 2 (9 +4)

= 2 (13)

= 26

A

= 2(9) + 2 (4)

= 18 + 8

= 26

B

= 2(13)

= 26

C

= 18 + 8

= 26

D

= 22

D does not apply because it does not equal 26

Answer:

It can be written as 825/1000. You can simplify this to get the simplest form which would be 33/40. All decimals are out of one, they are a part. When you first get a decimal, put the numbers such as 825 on top. The last number is in the thousandths place, so it is out of 1000. 1000 is your denominator. Your fraction is then 825/1000. From here you can simplify if possible.

Hope this helps ^-^

Answer:

√135

Step-by-step explanation:

3^2+b^2=12^2

9+b^2=144

9-9+b^2=144-9

b^2=135

√135=b

Answer:

3                     sqrt(3)

-----------    or  -----------

2 sqrt(3)            2

Step-by-step explanation:

3 sqrt(8)

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

4 sqrt(6)

3 sqrt(4*2)

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

4 sqrt(3*2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

3 sqrt(4) sqrt(2)

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

4 sqrt(3) sqrt(2)

Canceling the sqrt(2) and sqrt(4) is 2

3*2

----------

4 sqrt(3)

3

-----------

2 sqrt(3)

We can simplify the answer be multiplying by sqrt(3)/sqrt(3)

3                 sqrt(3)

----------- * ----------

2 sqrt(3)     sqrt(3)

3 sqrt(3)

-----------

2 *3

sqrt(3)

-----------

2

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+2&(1)\\3x=-y+10&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\3x=-(5x+2)+10\\3x=-5x-2+10\qquad\text{add 5x to both sides}\\8x=8\qquad\text{divide both sides by 8}\\x=1\\\\\text{put the value of x to (1):}\\\\y=5(1)+2\\y=5+2\\y=7[/tex]

Answer:

- 3, 9, 25

Step-by-step explanation:

To find the required terms of the sequence substitute n = 2, 5, 9 into the given rule, that is

[tex]a_{2}[/tex] = - 7 + (2 - 1)4  = - 7 + (1 × 4) = - 7 + 4 = - 3

[tex]a_{5}[/tex] = - 7 + (5 - 1)4 = - 7 + (4 × 4) = - 7 + 16 = 9

[tex]a_{9}[/tex] = - 7 + (9 - 1)4 = - 7 + (8 × 4) = - 7 + 32 = 25

The second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.

The second, fifth, and ninth terms of the sequence defined by the formula an = -7 + (n - 1) * 4 are -3, 9, and 25, respectively.

To find the second, fifth, and ninth terms of the sequence given by the formula an = -7 + (n - 1) * 4, we can simply plug the corresponding values of n into the formula.

For the second term (a2), where n=2:

a2 = -7 + (2 - 1) * 4

a2 = -7 + 1 * 4

a2 = -7 + 4

a2 = -3

For the fifth term (a5), where n=5:

a5 = -7 + (5 - 1) * 4

a5 = -7 + 4 * 4

a5 = -7 + 16

a5 = 9

For the ninth term (a9), where n=9:

a9 = -7 + (9 - 1) * 4

a9 = -7 + 8 * 4

a9 = -7 + 32

a9 = 25

Therefore, the second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.

Answer:

[tex]\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}[/tex]

Step-by-step explanation:

[tex](-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}[/tex]

Final answer:

To simplify (-3c⁻³w⁵)³, you must distribute the power of 3 to each factor inside the parenthesis and apply the rule for negative exponents to end up with -27w¹⁵/c⁹, which is answer choice D.

Explanation:

The expression to simplify is  (-3c⁻³w⁵)³. We will apply the rule for exponents to simplify the expression. When applying this rule and the negative exponent rule which states that a⁻ⁿ = 1/aⁿ, we get:

The correct answer is D.  -27w¹⁵/c⁹.

Answer:

y-int:3

slope:-3

Step-by-step explanation:

6x-2y=-6

change to y=mx+b: -2y=-6x-6

divide by -2

y=3x+3

The answer is c $92,598

Answer:

$92,598

Step-by-step explanation:

The purchaser pays Ben $20,000 today and then $20,000 every year for the next 4 years.

The interest rate is 4% per annum.

So the net present value of all the payments is :

20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)

= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08

= 92597.7

= 92,598 (approx)

So the net present value of all the payments made to Ben is $92,598.

Answer:

1 3/4 t -7/2

Step-by-step explanation:

t + 3/4t - 7/2

Get a common denominator for the t terms, which is 4

4/4t + 3/4t - 7/2

7/4 t -7/2

This is an improper fraction so change it to a mixed number

1 3/4 t -7/2