A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.) How many ounces of almonds would be in a one-pound bag (16 ounces) of this trail mix?

Answer:

Step-by-step explanation:

Hope this helps u!!

The expression, written as the sine of an angle is sin (7π/10)

From the question, we are to write the given expression as the sine or cosine of an angle.

The given expression is

sin(π/5)cos(π/2) + sin(π/2)cos(π/5)

Let A = π/5

and

B = π/2

Thus, we get

sinA cosB + sinB cosA

From the given information, we have that

sin(A ± B) = sinA cos B ± cosA sinB

∴ sin(A + B) = sinA cos B + cosA sinB

Now,

sinA cosB + sinB cosA = sinA cosB + cosA sin B

∴ sinA cosB + sinB cosA = sin (A + B)

Put A = π/5

and

B = π/2

sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)

sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)

Hence, the expression, written as the sine of an angle is sin (7π/10)

Learn more on Trigonometry identities here: https://brainly.com/question/12994136

#SPJ1

The blanks in this two-column proof should be completed (filled) as follows:

Statements                              Reasons_______________

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.

In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.

Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.

Read more on CPCTC here: https://brainly.com/question/6076251

#SPJ1

Answer:

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

Step-by-step explanation:

or what the  guy said on top :D

Answer:

aₙ = 2n+ 3

Step-by-step explanation:

The general equation for the nth term of an arithmetic series with  common difference d and first term a(1) is given by

aₙ = a₁  + d(n - 1)

Using values for the 5th and 15th terms we get

a₅ = a₁ + d(5 -1) = 13
==> a₁ + 4d = 13     (1)

a₁₅ = a₁ + d(15 - 1) = 33
a₁ + 14d = 33         (2)

Eq (2) - Eq(1) gives us:
a₁ + 14d - (a₁ + 4d) = 33 - 13

a₁ + 14d - a₁  - 4d  = 20

a₁ - a₁ + 14d - 4d =20

10d = 20

d = 2

Plugging d = 2 in (1) we get:
a₁ + 4(2) = 13
a₁ + 8 = 13

a₁ = 13 - 8 =5

So first term is 5,common difference is 2

Expression for nth term:
aₙ = 5 + 2(n - 1)

aₙ = 5 + 2n - 2

aₙ = 2n+ 3

Answer:

Part A

positive=132

negative=220

Part B=88

Step-by-step explanation:

Part A

3:5

positive: negative

3+5=8

352/8=44

3x44=132 positive or 3/8 of 352

5x44=220 negative 5/8 0f 352

Part B

220

-132

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

     88

Answer:

Third option) m = - \(\frac{1}{3}\)

Step-by-step explanation:

[] Slope is change in y over change in x or rise over run

[] Since we have a graph with easy-to-read points, I will use rise over run

-> I will choose the point (-1, 5)

-> I count down 1 unit to the y-axis of point (2, 4)

-> I count right 3 units to point (2, 4)

-> I get a slope of 1/3

[] Since the line is going from top left to bottom right, it'll be negative

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

If \(\sim q1, . . . ,\sim qn\) are the columns of a unitary matrix q, they must be linearly independent.

To show that if \(\sim q1, . . . ,\sim qn\) are the columns of a unitary matrix q, they must be linearly independent, we need to demonstrate that there are no nontrivial solutions to the equation \(c1\sim q1 + c2\sim q2 + ... + cn\sim qn = 0\), where c1, c2, ..., cn are complex scalars.

Assume that the columns \(\sim q1, . . . ,\sim qn\) are linearly dependent, meaning that there exist complex scalars c1, c2, ..., cn, not all zero, such that  \(c1\sim q1 + c2\sim q2 + ... + cn\sim qn = 0\).

Since the columns of the unitary matrix q are orthogonal, taking the inner product of both sides of the equation with the conjugate transpose of q yields:

\((q^H)(c1\sim q1 + c2\sim q2 + ... + cn\sim qn) = (q^H)0\),

where \((q^H)\) represents the conjugate transpose of q. By applying the properties of the conjugate transpose, we have:

\(c1(q^H)q1 + c2(q^H)~q2 + ... + cn(q^H)~qn = 0\).

Since \((q^H)~qi = 1\)for every i, the equation simplifies to:

c1 + c2 + ... + cn = 0.

However, this contradicts our assumption that c1, c2, ..., cn are not all zero, as it implies a nontrivial solution to the equation. Therefore, we can conclude that the columns \(\sim q1, . . . ,\sim qn\) must be linearly independent.

In conclusion, if \(\sim q1, . . . ,\sim qn\) are the columns of a unitary matrix q, they must be linearly independent. This can be proven by assuming that the columns are linearly dependent and then showing that this leads to a contradiction. Therefore, the statement holds true.

To know more about linearly independent visit:

brainly.com/question/14351372

#SPJ11

The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.

The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD,

where

D = 100k,

L = 140k, L < 100psf,

Lr = 40k,

W = +160k or −100k, and

E = +180k or −125k is given below:

Design load = 1.2D + 1.6(Lr or S or R) + 0.5(L + Lr or R) + (W or E)

Here, D is the weight of dead load, L is the weight of live load, Lr is the weight of the roof live load, W is the weight of wind load and E is the weight of earthquake load.

Therefore, for the given loads,

D = 100k

L = 140k

Lr = 40k

W = +160k or −100k

E = +180k or −125k

Max load = 1.2D + 1.6(Lr) + 0.5(L + Lr) + W

= 1.2 (100) + 1.6 (40) + 0.5 (140 + 40) + 160

= 120 + 64 + 90 + 160

= 434 kips

Therefore, the maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.

To know more about expressions visit:

https://brainly.com/question/28170201

#SPJ11

Answer:

2 fifths 2/5

Step-by-step explanation:

10 sided dice has 10 possibilities so 7 8 9 10 are even or greater than 7 that's 4 out of 10 numbers but in simplest form would be 2/5 (2 fifths)

Answer: Hi!

4.89 * 2.2 = 10.758 (rounded is 10.76 or 10.8)

Tip: Line up the terms vertically and multiply.

Hope this helps!

we can substitute the side length into the formula for the area of an equilateral triangle to calculate the area.

To find the area of the equilateral triangle, we first need to determine the coordinates of its vertices.

Let's consider the vertex A of the equilateral triangle. Since it lies on the parabola defined by y = x^2, and it is parallel to the y-axis, its coordinates can be expressed as (x, x^2).

Since the triangle is equilateral, we can determine the coordinates of the other two vertices by rotating point A by 60 degrees clockwise and counterclockwise.

For the counterclockwise rotation, the coordinates of the second vertex B can be obtained by rotating point A by 60 degrees counterclockwise around the origin. Using the rotation formula, the coordinates of B will be:

B(x', y') = (xcos(60°) - x^2sin(60°), xsin(60°) + x^2cos(60°))

Similarly, for the clockwise rotation, the coordinates of the third vertex C can be obtained by rotating point A by 60 degrees clockwise around the origin. Using the rotation formula, the coordinates of C will be:

C(x'', y'') = (xcos(-60°) - x^2sin(-60°), xsin(-60°) + x^2cos(-60°))

Now, we have the coordinates of all three vertices of the equilateral triangle: A(x, x^2), B(x', y'), and C(x'', y''). To find the area of the triangle, we can use the formula for the area of an equilateral triangle:

Area = (sqrt(3) * side^2) / 4

In this case, the side length of the equilateral triangle can be determined by finding the distance between any two vertices.

Using the distance formula, the side length is given by:

side = sqrt((x' - x)^2 + (y' - x^2)^2)

To learn  more about triangle visit:

brainly.com/question/2773823

#SPJ11

If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

To learn more about MPC, visit:

https://brainly.com/question/14486062

#SPJ4

Answer:

B. 7

Step-by-step explanation: 6/24= 1/4 so 7/24>1/4

The integral is convergent. To evaluate it, we use the formula for the integral of e^x, which is e^x + C. So, integrating e^-6p gives us (-1/6)e^-6p. Evaluating this from 0 to infinity, we get: (-1/6)e^-6(infinity) - (-1/6)e^0.

Since e^-6(infinity) approaches 0 as p approaches infinity, the first term becomes 0. Therefore, the integral evaluates to: (-1/6)e^0 = -1/6, So the quantity converges to -1/6.To determine whether the given integral is convergent or divergent, we need to analyze the integral: ∫[2, ∞] e^(-6p) dp.

To evaluate this integral, we first apply the Fundamental Theorem of Calculus. We find the antiderivative of e^(-6p) with respect to p, which is (-1/6)e^(-6p). Now, we need to evaluate the limit: lim (b → ∞) [(-1/6)e^(-6p)] [2, b].

When we take the limit as b approaches infinity, e^(-6p) approaches 0 because the exponent becomes increasingly negative. Thus, the integral is convergent.

To find the value of the convergent integral, we can calculate: ((-1/6)e^(-6*2)) - ((-1/6)e^(-6*∞)) = (-1/6)e^(-12) - 0 = (-1/6)e^(-12), So, the integral is convergent, and its value is (-1/6)e^(-12).

To know more about theorem click here

brainly.com/question/30242664

#SPJ11

Answer:

$1,956.95

Step-by-step explanation:

The school bought 47 sandwiches for $40.60

= 47 × 40.60

= 1,908.2

They also bought 39 bags of chips for $1.25

= 1.25×39

= 48.75

Therefore the total amount spent can be calculated as follows

= 48.75 + 1,908.2

= 1,956.95

Hence the total amount spent by the school is $1,956.95

Answer:

B table

Step-by-step explanation:

The B table is a linear table because with each x value, the y value is moving steadily with addition/subtraction. Table A is moving steadily with multiplication.

The nth term of the sequence whose integers are between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹

Consecutive numbers are those numbers that succeed each other in increasing order from least to greatest. The numbers that are given:

Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:

Then, the number of n can be computed as n!

= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

= 1.254 × 10¹¹

Learn more about consecutive numbers here:
https://brainly.com/question/26352026

The nth term of the series of integers is between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹

Consecutive numbers are those numbers that succeed by each other in increasing order from lowest to greatest such are 1, 2, 3, 4, 5, 6, or 7.

Now, suppose n represents the number of n-digit positive integers.

1, 2, 3, 4, 5, 6, or 7 with the permission of repetition no two consecutive digits are even.

Then, the number of n can be calculated as n!

= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

= 1.254 × 10¹¹

Learn more about consecutive numbers here:

brainly.com/question/26352026

#SPJ4

Answer:

12.50

Step-by-step explanation:

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

To learn more about algebraic expression, refer to the link-

https://brainly.com/question/2164351

#SPJ1

Total cost of items Mark bought = $8.80

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Price of the items, $3.25, $0.55, $2.95, and $4.25 before tax.

Total price = $11

Discount on items = 20%

Discount = (20/100)11 = $2.20

Cost of the items = $11 - $2.20 = $8.80

Hence, $8.80 is total cost of items Mark bought.

Learn more about percentage here:

https://brainly.com/question/29306119

#SPJ1

The equation of the bouncing ball is h(t) = 4sin(86t), where h(t) is the height of the ball in meters, and t is the time in seconds. We are supposed to find the first time the ball reaches a height of 2 meters.

To find the time taken by the ball to reach a height of 2 meters,

we need to equate the equation h(t) to 2 and solve for t as shown below:

2 = 4sin(86t)

Dividing both sides of the equation by 4, we have;

sin(86t) = 1/2Now we have to find the angle whose sine is 1/2 using the table of exact values of trigonometric ratios.

Since sin 30° = 1/2,

we can write the equation as:

= 30°To get the value of t,

we can solve for t as follows:

t = 30°/86t = 0.349s

The first time the ball reaches a height of 2 meters is 0.349 seconds.

To know more about trigonometric ratios visit:

https://brainly.com/question/23130410

#SPJ11

Answer:

30 hours

Step-by-step explanation:

so i did 396.10/ 17, and i got 23.3 then u divide his hourly pay by 699.00 and u got 30

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

Learn more about Cube here https://brainly.com/question/14619542

#SPJ4

Step-by-step explanation:

He probably forgot to finish the equation.

he started right: 180° - 55° = 125°

but he should have continued 125° = a + b; a = 90° (right angle) b = 125° - 90° = 35°

Answer:

Kate is 3 years old, Jane is 9 years old

Step-by-step explanation:

1.) First, assign variables to all of their ages. If we say Kate's age is x, Jane's age is 3 times this, which can be written as j, is 3x.

2.) Jane's age is also 2 less than twice of Kate's in 5 years. This means that her age is also 2(x+5) - 2 = j + 5. With a little simplification, you get that 2x + 8 = j + 5.

3.) Since j, Jane's age, is also 3x, we can substitute 3x in for j in the second equation. If you do this, you get 2x + 8 = 3x + 5.

4.) By moving the x onto one side and the numbers onto another, you get x = 3. X was Kate's age, meaning that Kate is 3 years old.

5.) Finally, since Jane's age is 3 times Kate's age, Jane's age is 3 * 3, which is 9. Jane is 9 years old.

Jane is 9 years old and Kate is 3 years old.To solve the problem, let's first establish variables for Jane and Kate's ages.

Let J represent Jane's age and K represent Kate's age.
According to the student question, Jane is 3 times as old as Kate, which can be represented as:
J = 3K
In 5 years, Jane's age will be 2 less than twice Kate's age, which can be represented as:
J + 5 = 2(K + 5) - 2
Now we can solve the equations step by step:

Substitute the first equation into the second equation to eliminate one of the variables:
3K + 5 = 2(K + 5) - 2
Distribute the 2 on the right side of the equation:
3K + 5 = 2K + 10 - 2
Simplify the equation by combining like terms:
3K + 5 = 2K + 8
Move the 2K term to the left side of the equation:
K = 3
now we know that Kate is currently 3 years old.
Substitute K's value back into the first equation to find Jane's age:
J = 3K
J = 3(3)
Simplify to find Jane's age:
J = 9
So, Jane is currently 9 years old.
Jane is 9 years old and Kate is 3 years old.

for more questions on variables

https://brainly.com/question/9302141

#SPJ11

(v) To prove that 0<1, we start by assuming the opposite, i.e., that 1≤0. Then, by property (i), we have -1 ≤ 0. But then, by property (iii), we have (-1)*(-1) = 1 ≤ 0, which is a contradiction to our assumption. Therefore, it must be the case that 0<1.

(vii) To prove that if 0<a<b, then 0<1/b<1/a, we first note that a and b are both positive, since they are greater than 0. Then, by property (vi), we have 0 < b-a. Adding a to both sides gives us a < b, which we can rearrange as:

1/b < 1/a

Multiplying both sides by -1 gives us:

-1/a < -1/b

By property (i), we have -b ≤ -a, which means that -1/b ≤ -1/a. Since -1/b and -1/a are both negative, we can multiply both sides by -1 to get:

0 < 1/b < 1/a

Therefore, if 0<a<b, then 0<1/b<1/a, as required.

These proofs rely on the properties of an ordered field, particularly properties (i), (iii), (vi), and (vii). These properties allow us to reason about the order of numbers and their relationships with each other. By using these properties, we were able to prove that 0<1 and that if 0<a<b, then 0<1/b<1/a.

learn more about contradiction here

https://brainly.com/question/28568952

#SPJ11

Answer:

I think the next one 400

Answer:

More than two factors

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

more than 2 answers

Stay safe,wear a mask,stay at home <3