Rachel, Adam, Michelle, Hannah, and James are going to the movies. They have $65 to spend on tickets and snacks. Each movie ticket costs $9.50, and each snack item costs $4.50. How many snacks can they buy to split among them? This problem is modeled by the inequality 5(9.5) + 4.5x ? 65, which is equal to 47.5 + 4.5x ? 65. The first step in solving the inequality is to . The second step is to . The five friends will have to split snacks.

Answer:

The least amount of large plate packs that would have to be purchased is 24.

Step-by-step explanation:

To do this we have to find first multiplication of 8 that is equally divided by 12.

A person can buy large packs of plates in multiple of 12 only.

A person can buy {1,2,3,4,5,6,7,8,...}packs of plates and will purchase

{12,24,36 ,48,60,72,84,96,...}large plates.

A person can buy small packs of plates in multiple of 8 only.

A person can buy {1,2,3,4,5,6,7,8,9,10,11,12...}packs of plates and will purchase..

{8,16,24,32,40,48,56,64,72,80,88,96,...}small plates

Now we have to keep in mind that one has to purchase equal amount of plates..

A person can buy {24,48,72,96} plates and hence least amount of large plate packs that would have to be purchased is 24....

if it is asking for compound interest your answer should be 49761.9

D using the foil method

Answer: [tex]4x^2+17x-15[/tex]

Step-by-step explanation:

To simplify the given expression we need to apply the distributive property in algebra.

The distributive property is given by :

[tex]a(b+c)=ab+ac[/tex]

The given expression:

[tex](4x- 3)(x + 5)\\\\=(4x-3)x+(4x-3)5\ \ \ \ \text{By distributive property}\\\\=4x^2-3x+20x-15\\\\=4x^2+(-3+20)x-15\ \ \ \text{Combining like terms}\\\\=4x^2+17x-15[/tex]

Answer:

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}[/tex]

We have:

[tex]DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788[/tex]

Substitute:

[tex]\dfrac{75}{0.9659}=\dfrac{EF}{0.788}[/tex]          cross multiply

[tex]0.9659EF=(75)(0.788)[/tex]

[tex]0.9659EF=59.1[/tex]          divide both sides by 0.9659

[tex]EF\approx61.19[/tex]

The length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have:

DE = 75 inches

By using the sin law:

sin52/EF = sin75/DE

sin52/EF = sin75/75

sin52/EF = 0.0128

EF = 61.185 ≈ 61.19 inches

Thus, the length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

Answer:

300%

Step-by-step explanation:

600 / 120 = 300

Answer:

wouldn't it be 6/5 or 5/6 or 1.2

Step-by-step explanation:

The scenario involves differentiating a proportional relationship between the woman's distance from a streetlight and the length of her shadow to determine the rate of change of the shadow's length and the speed of the shadow's tip.

The question involves finding the rates of change in the scenario where a woman walks toward a streetlight and the effects on her shadow's length and speed. Let's denote the distance between the woman and the streetlight as x, the length of her shadow as y, and her height as h. The streetlight's height is given as H. Using similar triangles, we can establish the relationship (H - h) / y = H / (x + y). Differentiating both sides with respect to time, t, allows us to calculate the rates of change we're interested in.

To find the rate of change of her shadow's length when she is 16 feet from the streetlight, we can take dh/dt as 0 since her height is constant, dx/dt as -4 ft/s because she is walking towards the light and substitute into the derived equation after differentiating. Similarly, we calculate the rate at which the tip of the shadow is moving by adding the rate of the woman's movement to the rate of change of the shadow's length.

ANSWER

[tex]y = - 5[/tex]

EXPLANATION

The horizontal asymptote of a general exponential function,

[tex]f(x) = a {(b)}^{x} + c[/tex]

is y=c.

The given exponential function is

[tex]f(x) = 4{(2)}^{x} - 5[/tex]

By comparing the given function to

[tex]f(x) = a {(b)}^{x} + c[/tex]

we have c=-5, therefore the horizontal asymptote is

[tex]y = - 5[/tex]

Answer:

(3250/100)*80 = $ 2600 - 3250 = $650

Step-by-step explanation:

Answer:

The answer is C) -1 and -4

Step-by-step explanation:

Sorry i don't have the step by step explanation but that's the answer

The answer is: True.

A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.

So:

[tex]sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx[/tex]

Then, evaluating we have:

[tex]\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}[/tex]

Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for [tex]sec^{2}x-1=\frac{cosx}{cscx}[/tex] and the answer is true.

Have a nice day!

Answer:

6x-5y=-10

Step-by-step explanation:

We are given an equation in words and we are to translate it and then re-write its standard form:

'y space equals space 6 over 5 x space plus space 2 '

[tex] y = \frac { 6 } { 5 } x + 2 [/tex]

Re-arranging this given equation to get:

[tex] y - 2 = \frac { 6 } { 5 } x [/tex]

[tex]5(y-2)=6x[/tex]

[tex]5y-10=6x[/tex]

[tex]6x-5y=-10[/tex]

So the correct answer option is 6x-5y=-10.

Answer:

B. x = 4

Step-by-step explanation:

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

[tex]\log_bm+\log_bn=\log_bmn[/tex]

Using this law, we can combine and rewrite our initial equation as

[tex]\log_2(x\cdot(x-2))=3\\\log_2(x^2-2x)=3[/tex]

Remember that logarithms are simply another way of writing exponents. The logarithm [tex]\log_28=3[/tex] is just another way of writing the fact [tex]2^3=8[/tex]. Keeping that in mind, we can express our logarithm in terms of exponents as

[tex]\log_2(x^2-2x)=3\rightarrow2^3=x^2-2x[/tex]

2³ = 8, so we can replace the left side of our equation with 8 to get

[tex]8 = x^2-2x[/tex]

Moving the 8 to the other side:

[tex]0=x^2-2x-8[/tex]

We can now factor the expression on the right to find solutions for x:

[tex]0=(x-4)(x+2)\\x=4, -2[/tex]

The only option which agrees with our solution is B.

Answer:

The answer is:

        [tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]

Step-by-step explanation:

We are given a logarithmic expression as:

[tex]\log_2 x+log_2 (x-2)=3[/tex]

As we know that:

[tex]\log_a x=\dfrac{\log x}{\log a}[/tex]

Hence, we get the logarithmic expression as follows:

[tex]\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}=3[/tex]

We know that we can get the system of equations as follows:

[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}[/tex]

and

[tex]y_2=3[/tex]

Hence, when we plot the graph for this system of equations we see that the point of intersection of the graph is: (4,3)

Hence, the solution is the x-value of the point of intersection of the two equations.

Hence, x=4 is the solution.

Hence, the correct option is:

  [tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]

simplify :7x + 3x - 5 + 8x + 5 = 180

x = 10

Here is your answer

[tex]<b>z= 20 degrees</b>[/tex]

REASON:

[tex]<font color="blue" size=5>Concept used</font>[/tex]: The sum of adjacent angles of a parallelogram is 180 degrees.

So, in above given figure

[tex] 2z+16+124=180 [/tex] (measures of adjacent angles)

[tex]2z+140=180 [/tex]

[tex] 2z=180-140 [/tex]

[tex]2z=40 [/tex]

[tex]z= 40/2 [/tex]

[tex]z= 20 [/tex]

HOPE IT IS USEFUL

Answer:

No solution.

Step-by-step explanation:

The given functions are

[tex]y=\cos2x[/tex] and [tex]y=1-\sin^2x[/tex].

To find the point of intersections of the graphs of the two functions: we equate them and solve for [tex]x[/tex].

[tex]\cos2x=1-\sin^2x[/tex]

Recall the double angle identity; [tex]\cos2x=cos^2x-sin^2x[/tex]

Apply this identity to obtain;

[tex]cos^2x-sin^2x=1-\sin^2x[/tex]

[tex]\Rightarrow cos^2x=1[/tex]

[tex]\cos x=\pm1[/tex]

[tex]x=0\:or\:x=\pi[/tex]

if the interval is [tex]0\le x\le \pi[/tex], then the two graphs intersect at [tex]x=0\:or\:x=\pi[/tex]

But [tex]x=0\:and\:x=\pi[/tex] does not belong to the open interval [tex]0\:<\:x\:<\:\pi[/tex]

No point of intersection.

Answer:

$455.97

Step-by-step explanation:

119000 × 0.12 = 14280

119000 - 14280 = 104720

104720 × 1.045 = 109432.4

109432.4/(20×12)

109432.4/240

455.97 a month

Answer:

$662.46

Step-by-step explanation:

Answer:

a. Ratio of girls to all students 5:11

b. Ratio of girls to all students n:m+n

c. Ratio of girls to boys 5:6

Step-by-step explanation:

In order to find each of these, we simply need to look at these as a comparison of two data points.

a. In this example, we are looking for girls to all students. We already who there would be 5 girls in the comparison. Then we need to find the whole amount, which is girls + boys (6 + 5 = 11)

5:11

b. In this example, we are looking for girls to all students. We already who there would be n girls in the comparison. Then we need to find the whole amount, which is girls + boys (m + n)

n:m+n

c. In this example, we are looking for girls to boys. We already who there would be 5 girls in the comparison. Then we need to find the boys amount, which is whole - girls (11 - 5 = 6)

5:6

Final answer:

The ratio of girls to all students in a class with a boy-girl ratio of 6 to 5 is 5 to 11. The general ratio of girls to all students with a boy-girl ratio expressed as m:n is n:(m+n). Lastly, if five elevenths of the class are girls, then the ratio of girls to boys is 5 to 6.

Explanation:

Understanding Ratios in a Classroom Setting

The ratio of boys to girls in a class is initially given as 6 to 5. To find the ratio of girls to all the students in the class, the sum of the parts of the ratio must first be calculated, which is 6 (boys) + 5 (girls) = 11 (total students).

Therefore, the ratio of girls to the total number of students is 5 to 11. This is because for every 11 students, 5 are girls. If the ratio of boys to girls is expressed as m:n, then the ratio of girls to all students will be n:(m + n).

For a scenario where five elevenths of the class are girls, the ratio of girls to boys needs to be determined. As five elevenths represent the girls, six elevenths must represent the boys, since they sum up to the whole, which is one (or 11/11). Therefore, the ratio of girls to boys is 5:6.

1/2÷1/6

=

1/2*6/1

=

6/2

=

3

Answer:

Quotient would be 3.

Step-by-step explanation:

The model below can be used to find the quotient of one over two dividend by one over six.

We will rewrite the problem :

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

As we know when we divide the two fractions, we must invert the second fraction and put the sign of multiplication in place of division sign and multiply.

So now we can write the problem as :

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

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

= 3

Quotient would be 3.

Answer:

  90°

Step-by-step explanation:

Supplementary means they add to 180°. Vertical angles are congruent, so they must both be 180°/2 = 90°.

Answer:

90

Step-by-step explanation:

Did the Geometry quiz 2021

Plz click the Thanks button!

<Jayla>

The other root of the quadratic equation is -2, and the coefficient c is -106, found using the sum and product of roots formulas.

The other root and the coefficient c of the quadratic equation 10x²- 33x + c = 0, given that one of the roots is 5.3. Using the fact that the sum of the roots of a quadratic equation ax² + bx + c = 0 is equal to -b/a, we can find the other root. With one root known to be 5.3 and a = 10, b = -33, the sum of the roots must be 3.3. Therefore, the other root is 3.3 - 5.3 = -2. To find the coefficient c, we use the fact that the product of the roots of a quadratic equation is equal to c/a. Thus, c = 5.3 * (-2) * 10 = -106. The other root of the equation is -2, and the coefficient c is -106.

Answer:

YES

YES

NO

YES

Step-by-step explanation:

Assuming that the value is [tex]\dfrac{4}{9}[/tex].

Let's take each of the equations and check if the fraction makes the equation true.

When multiplying a whole number to a fraction, it is the same as multiplying the whole number to the numerator and dividing the total by the denominator.

[tex]63*\dfrac{4}{9}=28[/tex]

[tex]\dfrac{63*4}{9}=28[/tex]

[tex]\dfrac{252}{9}=28[/tex]

[tex]28=28[/tex]    YES

[tex]18*\dfrac{4}{9}=8[/tex]

[tex]\dfrac{18*4}{9}=8[/tex]

[tex]\dfrac{72}{9}=8[/tex]

[tex]8=8[/tex]    YES

[tex]96*\dfrac{4}{9}=42[/tex]

[tex]\dfrac{96*4}{9}=42[/tex]

[tex]\dfrac{384}{9}=42[/tex]

[tex]42.67=42[/tex]    NO

[tex]36*\dfrac{4}{9}=16[/tex]

[tex]\dfrac{36*4}{9}=16[/tex]

[tex]\dfrac{144}{9}=16[/tex]

[tex]16=16[/tex]    YES

Answer:

yes

yes

no

yes

hope this helps!!

Answer: [tex]x=-1[/tex]

Step-by-step explanation:

By the negative exponent rule, you have that:

[tex](\frac{1}{a})^n=a^{-n}[/tex]

By the exponents properties, you know that:

[tex](m^n)^l=m^{(nl)}[/tex]

Therefore, you can rewrite the left side of the equation has following:

[tex](\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}[/tex]

 Descompose 32 and 8 into its prime factors:

[tex]32=2*2*2*2*2=2^5\\8=2*2*2=2^3[/tex]

Rewrite:

[tex](\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}[/tex]

Then:

[tex](\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}[/tex]

As the base are equal, then:

[tex]-3(2x+7)=5(3x)[/tex]

Solve for x:

[tex]-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1[/tex]

Answer:

  a straight line: y = x -5, with a hole at (4, -1)

Step-by-step explanation:

The rational function can be simplified to ...

  [tex]f(x)=\dfrac{x^2-9x+20}{x-4}=\dfrac{(x-5)(x-4)}{(x-4)}\\\\f(x)=x-5\qquad\text{$x\ne 4$}[/tex]

The graph of this is a straight line, with a hole at x=4, where the function is not defined.

Answer:

the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287

Step-by-step explanation:

When conducting hypothesis tests, the P value tells you the probability of the results happening by random chance.  That's why we usually test against a very low alpha level, usually 1% or 5%.  

Here P = 28%, so there is a 28% chance that if we take a sample of athletes, about 1 out of 4 times there won't be a significant difference in GPA between males and females.

the answer is 942.because the formula is V=Bh. V=pir2h. so V= 3.14×5squared×12. so 3.14×25×12. 25×12=300. and 3.14×300=942

Answer:

  4 units

Step-by-step explanation:

The sides of the rectangle are parallel to the axes, so it is a simple matter to subtract coordinate values to find the dimensions.

Along the line y=7, the rectangle extends from -5 to 5, so has width 10.

Along the line x=5, the rectangle extends from 1 to 7, so has length 6.

The width is 10 - 6 = 4 units more than the length.

Answer: width=7 length =9

9-7=2

2 is the answer

Answer:D) 144

Step-by-step explanation:12*12=144

Answer:

the answer is 144

Step-by-step explanation:

Answer:

y= -2x/3+8

Step-by-step explanation:

find 2 points: (0,8) and (6,4)

substitute in y=ax+b

8=0a+b

b=8

4=6a+b

4=6a+8

6a=-4

a=-2/3