Anna has 1/2 pound of trail mix. She evenly divides the trail mix into 4 bags. How much is in each bag?

Answer:

B. the y -intercept is (0,3)

Step-by-step explanation:

The confirmed correct answer is -9%. Trust me.

Answer:

Option B = -9%

Step-by-step explanation:

Given : Given an exponential function for compounding interest, [tex]A(x) = P(.91)^x[/tex]

To find : What is the rate of change?  

Solution :

The general form of the exponential function is [tex]f(x)=a(1+r)^x[/tex]

Where,

r is the rate of change

if r> 1 then it is growth rate    

if r< 1 then it is decay rate.

Comparing given function with exponential function,

[tex]A(x) = P(.91)^x[/tex]

[tex]1+r=0.91[/tex]

[tex]r=0.91-1[/tex]

[tex]r=−0.09[/tex]

It is a decay rate.

Convert into percentage, multiply with 100

[tex]-0.09\times 100=-9\%[/tex]

Therefore, Option B is correct.

The rate of change is -9%.      

Answer:

Option D is correct

Step-by-step explanation:

Given Equations of Circles:

Circle 1 - [tex](x+12)^2+(y+16)^2=(r_1)^2[/tex]

Circle 2 -  [tex](x-30)^2+(y-16)^2=(r_2)^2[/tex]

Both circles passes through origin.

To find: Values of [tex]r_1\:,\:r_2[/tex]

Coordinates of origin = ( 0 , 0 )

Circles passes through origin means x = 0 & y = 0 must satisfy the equation of circles.

So, Substituting x = 0 &  y = 0 in Eqn of Circle 1

we get

[tex](0+12)^2+(0+16)^2=(r_1)^2[/tex]

[tex](r_1)^2=12^2+16^2[/tex]

[tex](r_1)^2=144+256[/tex]

[tex](r_1)^2=400[/tex]

[tex]r_1=\sqrt{400}[/tex]

[tex]r_1=20[/tex]

Now, Substituting x = 0 &  y = 0 in Eqn of Circle 2

we get

[tex](0-30)^2+(0-16)^2=(r_2)^2[/tex]

[tex](r_2)^2=(-30)^2+(-16)^2[/tex]

[tex](r_2)^2=900+256[/tex]

[tex](r_2)^2=1156[/tex]

[tex]r_2=\sqrt{1156}[/tex]

[tex]r_2=34[/tex]

Therefore, Option D is correct .i.e., [tex]r_1=20\:\:,\:\:r_2=34[/tex]

Answer:

Approximately 157.08 sq. cm.

Step-by-step explanation:

The Area of an Ellipse is given by the formula  [tex]A=\pi a b[/tex]

Here 2a = 10, so a = 5

Also, 2b = 20, b = 10

Substituting these into the area formula gives us:

[tex]A=\pi a b\\A=\pi (5)(10)\\A=50\pi\\A=157.08[/tex]

The Area is approximately 157.08 sq. cm.

Answer:

The number of steps in a stairway is discrete.

Step-by-step explanation:

A discrete data is that, which can take only integer values like number of apples in a basket.

But the continuous data is that, which can take on any value like a decimal. For example, the weight of patients in a hospital.

So, the number of steps in a stairway will be a discrete data. As stairs are counted in whole numbers and not decimals.

Answer:

B. False.

Step-by-step explanation:

We have been given an image of a quadrilateral. We are asked to determine whether a circle could be circumscribed about the given quadrilateral.

We know that opposite angles of a cyclic quadrilateral are supplementary.

Let us check is this true for our given quadrilateral or not.

[tex]m\angle B+m\angle D=180^{\circ}[/tex]

[tex]80^{\circ}+60^{\circ}=180^{\circ}[/tex]

[tex]140^{\circ}\neq 180^{\circ}[/tex]

Now let us check other pair of angles.

[tex]m\angle A+m\angle C=180^{\circ}[/tex]

[tex]110^{\circ}+110^{\circ}=180^{\circ}[/tex]

[tex]220^{\circ}\neq 180^{\circ}[/tex]

Since opposite angles of our given quadrilateral are not supplementary, therefore, a circle could not be circumscribed about the given quadrilateral.

Given is the borrowed amount = 380 dollars.

Repayment period = 6 months.

Monthly installments = 67 dollars.

After six months, total repaid amount would be sum of all six monthly installments i.e. 6 x 67 = 402 dollars.

The interest to be paid on this loan would be difference of total repaid amount and borrowed amount.

Interest paid = Repaid amount - Borrowed amount

Interest = 402 dollars - 380 dollars

Interest = 22 dollars.

So, he would pay 22 dollars as interest on this loan.

Answer:

[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]

Step-by-step explanation:

Given that a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

we have to find the area of pentagon.

Apothem=a=3 cm

Perimeter=s=21.8 cm

[tex]\text{Area of regular pentagon=}\frac{1}{2}\times apothem\times perimeter[/tex]

[tex]\frac{1}{2}\times s \times a[/tex]

[tex]=\frac{1}{2}\times 21.8\times 3[/tex]

[tex]=\frac{65.4}{2}=32.7 cm^2[/tex]

[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]

Option 3 is correct.

Answer:

[tex]^{10}C_5(2a)^{5}(-3b)^5[/tex]

Option 1 is correct.

Step-by-step explanation:

Given: [tex](2a-3b)^{10}[/tex]

We need to find 6th term of binomial expansion.

Formula:

[tex]T_{r+1}=^nC_rx^{n-r}y^{r}[/tex]

We need to find 6th term, [tex]T_6[/tex]

[tex]T_6=T_{r+1}[/tex]

So, r=5

Put r=5 into formula

[tex]n=10, x=2a \text{ and }y=-3b[/tex]

[tex]T_6=^{10}C_5(2a)^{10-5}(-3b)^5[/tex]

Now we will simplify it to calculate 6th term

[tex]T_6=^{10}C_5(2a)^{5}(-3b)^5[/tex]

Hence, The 6th term of binomial is [tex]^{10}C_5(2a)^{5}(-3b)^5[/tex]

The expression that represents the sixth term in the binomial expansion of (2a - 3b)¹⁰ is expressed as  ¹⁰C₆(2a)⁴(-3b)⁶.

To find the sixth term in the binomial expansion of (2a - 3b)¹⁰, we can use the binomial theorem,

which states that the k-th term in the expansion of (a + b)ⁿ can be calculated using the following formula:

T(x) = C(n, x) × (aⁿ⁻ˣ) × (bˣ)

Where:

T(x) is the x-th term in the expansion.

C(n, x) is the binomial coefficient, also denoted as "n choose x," and it is equal to n! / (x! × (n-x)!), where "!" denotes factorial.

a is the first term in the binomial (2a in this case).

b is the second term in the binomial (-3b in this case).

n is the exponent of the binomial (10 in this case).

x is the term we want to find (the sixth term in this case).

Now, let's calculate the sixth term:

x = 6

n = 10

a = 2a

b = -3b

First, calculate the binomial coefficient:

C(10, 6) = 10! / (6! × (10-6)!)

C(10, 6) = 210

Now, plug these values into the formula:

T(6) = 210 × (2a)¹⁰⁻⁶ × (-3b)⁶

Simplify the exponents:

T(6) = 210 × (2a)⁴ × (-3b)⁶

T(6) = 210 × 16a⁴× 729b⁶

Now, multiply the constants:

T(6) = 30,240a⁴b⁶

Therefore, the sixth term in the binomial expansion of (2a - 3b)¹⁰ is 30,240a⁴b⁶ which is written as ¹⁰C₆(2a)⁴(-3b)⁶.

learn more about binomial expansion here

brainly.com/question/32370598

#SPJ3

Answer:

The rocket is at a greater height when t = 3 than it is when t = 1.

Option B

Step-by-step explanation:

Just took the test

Answer:

B

Step-by-step explanation:

!

Answer: [tex]5\sqrt{2}\ in[/tex]

Step-by-step explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.

Let H be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 5 in.

Now applying Pythagoras theorem, we get

[tex]H^2=5^2+5^2=25+25\\\\\Rightarrow\ H^2=50\\\\\Rightarrow H=\sqrt{50}\\\\\Rightarrow H=5\sqrt{2}\ in[/tex]

Hence, the length of the hypotenuse = [tex]5\sqrt{2}\ in[/tex]

Answer is -2x^2+8-10 hope this helps!!!!

Answer:

360°

Step-by-step explanation:

I just took the test.

Answer:

greatest common factor the largest factor that any given numbers have in common

Step-by-step explanation:

so the answer is greatest common factor

Final answer:

Knowledge of prime and common factors is essential for finding the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers, a key element in simplifying fractions and understanding ratios.

Explanation:

Understanding prime and common factors is instrumental in finding the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers. The GCD is the highest number that divides evenly into each of the numbers in question. For example, the GCD of 48 and 60 is 12 since 12 is the largest number that can divide both 48 and 60 without leaving a remainder. Finding the GCD is crucial in simplifying fractions, solving problems involving ratios, and is also a fundamental concept in more advanced mathematics including algebra and number theory.

The process often involves factoring the numbers down to their prime factors, identifying the common primes, and then multiplying these common prime factors together to find the GCD. This method not only highlights the importance of prime numbers in the mathematical hierarchy but also underlines the indelible role of factorization in simplifying and solving numerical problems.

Answer:

To estimate 179% of 41 by rounding, use the expression

✔ 180%(40)

.

Using the distributive property, the expression is equivalent to

✔ (100%)(40) + (80%)(40)

.

179% of 41 is about

✔ 72

.

Step-by-step explanation:

Answer:

The answer is 5.

Step-by-step explanation:

The length of the diagonal of a square with side lengths 7√2 is approximately 14.1 units.

The length of the diagonal of a square can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides. Since a square has all sides equal, the length of each side can be represented as 7√2. Substituting this value into the Pythagorean theorem, we get:

Diagonal² = (7√2)² + (7√2)²

Diagonal² = 98 + 98 = 196

Taking the square root of 196, we find the length of the diagonal to be approximately 14 units. Rounding to the nearest tenth gives us 14.1 units.