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3 years ago

Hello please help help

Mathematics

1 answer:

irinina [24]3 years ago

5 0

9514 1404 393

Answer:

48°

Step-by-step explanation:

ΔACB is isosceles, so angles A and B have the same measure. The measure of angle C in that triangle is ...

∠C = 180° -2(69°) = 42°

Angle C in ΔCDE has the same measure. Angle D is the complement of that:

∠D = 90° -42° = 48°

_____

The relations we used are ...

the sum of angles in a triangle is 180°
base angles of an isosceles triangle are congruent
vertical angles are congruent
acute angles in a right triangle are complementary

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5 0

2 years ago

I need to know the surface area of these

anastassius [24]

9514 1404 393

Answer:

245 cm²

Step-by-step explanation:

The surface area of a cone is given by ...

SA = πr(r +s) . . . . where r is the radius, and s is the slant height

Filling in the given values, we have ...

SA = (3.14)(3 cm)(3 cm +23 cm) = (3.14)(3)(26) cm² ≈ 245 cm²

The surface area of the cone is about 245 cm².

6 0

3 years ago

Tony wants to make 36 party bags. Glitter pens come in packs of 6. Stickers come in sheets of 4, and balls come in packs of 3. W

Fofino [41]

Do 6•6=36
4•9=36
3•12=36
So the answer is 12

3 0

3 years ago

In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Calculate the lower confidence

Lyrx [107]

Answer:

The 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

Step-by-step explanation:

In a random sample of 300 boards the number of boards that fall outside the specification is 12.

Compute the sample proportion of boards that fall outside the specification in this sample as follows:

$\hat p =\frac{12}{300}=0.04$

The (1 - α)% confidence interval for population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The critical value of z for 95% confidence level is,

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.04\pm1.96\sqrt{\frac{0.04(1-0.04)}{300}}\\=0.04\pm0.022\\=(0.018, 0.062)\\\approx(1.8\%, 6.2\%)$

Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

6 0

3 years ago

A geometric sequence is defined by the general term tn = 75(5n), where n ∈N and n ≥ 1. What is the recursive formula of the sequ

andreyandreev [35.5K]

The correct answer is C) t₁ = 375, $t_n=5t_{n-1}$ .

From the general form,
$t_n=75(5)^n$ , we must work backward to find t₁.

The general form is derived from the explicit form, which is
$t_n=t_1(r)^{n-1}$ . We can see that r = 5; 5 has the exponent, so that is what is multiplied by every time. This gives us

$t_n=t_1(5)^{n-1}$

Using the products of exponents, we can "split up" the exponent:
$t_n=t_1(5)^n(5)^{-1}$

We know that 5⁻¹ = 1/5, so this gives us
$t_n=t_1(\frac{1}{5})(5)^n
\\
\\=\frac{t_1}{5}(5)^n$

Comparing this to our general form, we see that
$\frac{t_1}{5}=75$

Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375

The recursive formula for a geometric sequence is given by
$t_n=t_{n-1}(r)$ , while we must state what t₁ is; this gives us

$t_1=375; t_n=t_{n-1}(5)$

3 0

3 years ago